Hayashi, Nakao; Naumkin, Pavel I. Modified scattering for the fractional mKdV equation. (English) Zbl 1523.35044 J. Evol. Equ. 23, No. 3, Paper No. 61, 37 p. (2023). MSC: 35B40 35Q53 35R11 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, J. Evol. Equ. 23, No. 3, Paper No. 61, 37 p. (2023; Zbl 1523.35044) Full Text: DOI
Carreño-Bolaños, Rafael; Hayashi, Nakao; Naumkin, Pavel I. Asymptotics of solutions for the fractional modified Korteweg-de Vries equation of order \(\alpha \in (2,3)\). (English) Zbl 1518.35078 SN Partial Differ. Equ. Appl. 4, No. 4, Paper No. 26, 15 p. (2023). MSC: 35B40 35Q53 35R11 PDFBibTeX XMLCite \textit{R. Carreño-Bolaños} et al., SN Partial Differ. Equ. Appl. 4, No. 4, Paper No. 26, 15 p. (2023; Zbl 1518.35078) Full Text: DOI
Carreño-Bolaños, Rafael; Naumkin, Pavel I. Large time asymptotics for the fractional modified Korteweg-de Vries equation of order \(\alpha \in \left[ 4,5\right)\). (English) Zbl 1518.35079 J. Pseudo-Differ. Oper. Appl. 14, No. 3, Paper No. 42, 28 p. (2023). MSC: 35B40 35Q53 35R11 PDFBibTeX XMLCite \textit{R. Carreño-Bolaños} and \textit{P. I. Naumkin}, J. Pseudo-Differ. Oper. Appl. 14, No. 3, Paper No. 42, 28 p. (2023; Zbl 1518.35079) Full Text: DOI
Naumkin, Pavel I.; Villela-Aguilar, José de Jesús Asymptotics of solutions to periodic problem for the Korteweg-de Vries-Burgers equation. (English) Zbl 07779120 Stud. Appl. Math. 149, No. 2, 523-536 (2022). Reviewer: Piotr Biler (Wrocław) MSC: 35Q53 35B10 35B40 PDFBibTeX XMLCite \textit{P. I. Naumkin} and \textit{J. de J. Villela-Aguilar}, Stud. Appl. Math. 149, No. 2, 523--536 (2022; Zbl 07779120) Full Text: DOI OA License
Hayashi, Nakao; Naumkin, Pavel I.; Sánchez-Suárez, Isahi Large time asymptotics for the fractional modified Korteweg-de Vries equation with \(\alpha \in \left(2,4\right)\). (English) Zbl 1501.35059 SN Partial Differ. Equ. Appl. 3, No. 6, Paper No. 76, 28 p. (2022). MSC: 35B40 35Q53 35R11 PDFBibTeX XMLCite \textit{N. Hayashi} et al., SN Partial Differ. Equ. Appl. 3, No. 6, Paper No. 76, 28 p. (2022; Zbl 1501.35059) Full Text: DOI
Hayashi, Nakao; Naumkin, Pavel I.; Sánchez-Suárez, Isahi Asymptotics for the modified Whitham equation. (English) Zbl 1397.35210 Commun. Pure Appl. Anal. 17, No. 4, 1407-1448 (2018). MSC: 35Q35 35Q55 35B40 35Q53 76B55 PDFBibTeX XMLCite \textit{N. Hayashi} et al., Commun. Pure Appl. Anal. 17, No. 4, 1407--1448 (2018; Zbl 1397.35210) Full Text: DOI
Hayashi, Nakao; Naumkin, Pavel I. Large time asymptotics of solutions for the third-order nonlinear Schrödinger equation. (English) Zbl 1360.35247 J. Math. Sci., Tokyo 23, No. 4, 867-919 (2016). MSC: 35Q55 35B40 35Q53 35B45 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, J. Math. Sci., Tokyo 23, No. 4, 867--919 (2016; Zbl 1360.35247) Full Text: Link
Hayashi, Nakao; Naumkin, Pavel I. Large time asymptotics for the Kadomtsev-Petviashvili equation. (English) Zbl 1318.35098 Commun. Math. Phys. 332, No. 2, 505-533 (2014). Reviewer: Ti-Jun Xiao (Fudan) MSC: 35Q53 35B40 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, Commun. Math. Phys. 332, No. 2, 505--533 (2014; Zbl 1318.35098) Full Text: DOI
Hayashi, Nakao; Naumkin, Pavel I. Scattering operator for nonlinear Klein-Gordon equations. (English) Zbl 1182.35198 Commun. Contemp. Math. 11, No. 5, 771-781 (2009). MSC: 35Q53 35L70 35A22 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, Commun. Contemp. Math. 11, No. 5, 771--781 (2009; Zbl 1182.35198) Full Text: DOI
Hayashi, Nakao; Naumkin, Pavel I. The initial value problem for the cubic nonlinear Klein-Gordon equation. (English) Zbl 1190.35199 Z. Angew. Math. Phys. 59, No. 6, 1002-1028 (2008). MSC: 35Q53 35Q55 35B40 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, Z. Angew. Math. Phys. 59, No. 6, 1002--1028 (2008; Zbl 1190.35199) Full Text: DOI
Hayashi, Nakao; Naumkin, Pavel I. Scattering operator for nonlinear Klein-Gordon equations in higher space dimensions. (English) Zbl 1136.35079 J. Differ. Equations 244, No. 1, 188-199 (2008). Reviewer: Ricardo Weder (México City) MSC: 35Q53 35P25 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, J. Differ. Equations 244, No. 1, 188--199 (2008; Zbl 1136.35079) Full Text: DOI
Hayashi, Nakao; Kaikina, Elena I.; Naumkin, Pavel I. Large time asymptotics for the BBM-Burgers equation. (English) Zbl 1131.35071 Ann. Henri Poincaré 8, No. 3, 485-511 (2007). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 35Q53 35B40 PDFBibTeX XMLCite \textit{N. Hayashi} et al., Ann. Henri Poincaré 8, No. 3, 485--511 (2007; Zbl 1131.35071) Full Text: DOI
Hayashi, Nakao; Naumkin, Pavel I. Asymptotics for the Korteweg-de Vries-Burgers equation. (English) Zbl 1104.35046 Acta Math. Sin., Engl. Ser. 22, No. 5, 1441-1456 (2006). MSC: 35Q53 35B40 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, Acta Math. Sin., Engl. Ser. 22, No. 5, 1441--1456 (2006; Zbl 1104.35046) Full Text: DOI
Kaikina, Elena I.; Naumkin, Pavel I.; Shishmarev, Ilya A. Periodic problem for a model nonlinear evolution equation. (English) Zbl 1057.35055 Adv. Differ. Equ. 7, No. 5, 581-616 (2002). Reviewer: Ángel Calsina (Girona) MSC: 35Q53 35B40 35S10 35Q55 PDFBibTeX XMLCite \textit{E. I. Kaikina} et al., Adv. Differ. Equ. 7, No. 5, 581--616 (2002; Zbl 1057.35055)
Kaikina, Elena; Kato, Keiichi; Naumkin, Pavel I.; Ogawa, Takayoshi Wellposedness and analytic smoothing effect for the Benjamin-Ono equation. (English) Zbl 1021.35098 Publ. Res. Inst. Math. Sci. 38, No. 3, 651-691 (2002). Reviewer: Igor Andrianov (Köln) MSC: 35Q53 35B65 PDFBibTeX XMLCite \textit{E. Kaikina} et al., Publ. Res. Inst. Math. Sci. 38, No. 3, 651--691 (2002; Zbl 1021.35098) Full Text: DOI
Hayashi, Nakao; Naumkin, Pavel On the modified Korteweg–de Vries equation. (English) Zbl 0994.35107 Math. Phys. Anal. Geom. 4, No. 3, 197-227 (2001). MSC: 35Q53 35B40 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. Naumkin}, Math. Phys. Anal. Geom. 4, No. 3, 197--227 (2001; Zbl 0994.35107) Full Text: DOI
Hyashi, Nakao; Matos, Tonatiuh; Naumkin, Pavel I. Large time behavior of solutions of higher order nonlinear dispersive equations of KdV type with weak nonlinearity. (English) Zbl 1022.35058 Differ. Integral Equ. 12, No. 1, 23-40 (1999). Reviewer: Mirko Rokyta (Praha) MSC: 35Q53 35B40 35S05 PDFBibTeX XMLCite \textit{N. Hyashi} et al., Differ. Integral Equ. 12, No. 1, 23--40 (1999; Zbl 1022.35058)
Hayashi, Nakao; Naumkin, Pavel I.; Saut, Jean-Claude Asymptotics for large time of global solutions to the generalized Kadomtsev-Petviashvili equation. (English) Zbl 0936.35158 Commun. Math. Phys. 201, No. 3, 577-590 (1999). Reviewer: T.A.Dzhangveladze (Tbilisi) MSC: 35Q53 35B40 PDFBibTeX XMLCite \textit{N. Hayashi} et al., Commun. Math. Phys. 201, No. 3, 577--590 (1999; Zbl 0936.35158) Full Text: DOI
Hayashi, Nakao; Naumkin, Pavel I. Asymptotics and scattering problem for the generalized Korteweg-de Vries equation. (English) Zbl 0939.35169 RIMS Kokyuroku 1059, 101-109 (1998). MSC: 35Q53 37K15 35B40 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, RIMS Kokyuroku 1059, 101--109 (1998; Zbl 0939.35169)
Hayashi, Nakao; Naumkin, Pavel I. Large time asymptotics of solutions to the generalized Korteweg-de Vries equation. (English) Zbl 0915.35093 J. Funct. Anal. 159, No. 1, 110-136 (1998). MSC: 35Q53 35B40 PDFBibTeX XMLCite \textit{N. Hayashi} and \textit{P. I. Naumkin}, J. Funct. Anal. 159, No. 1, 110--136 (1998; Zbl 0915.35093) Full Text: DOI
Naumkin, P. I. Evolution of a step for the Benjamin-Bona-Mahony-Burgers equation. (English. Russian original) Zbl 0965.35150 Dokl. Math. 55, No. 1, 144-147 (1997); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 352, No. 6, 742-745 (1997). MSC: 35Q53 76D33 PDFBibTeX XMLCite \textit{P. I. Naumkin}, Dokl. Math. 55, No. 1, 742--745 (1997; Zbl 0965.35150); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 352, No. 6, 742--745 (1997)
Naumkin, P. I.; Shishmarev, I. A. Asymptotics as \(t\to\infty\) of the solutions of nonlinear equations with nonsmall initial perturbations. (English. Russian original) Zbl 0881.35016 Math. Notes 59, No. 6, 618-624 (1996); translation from Mat. Zametki 59, No. 6, 855-864 (1996). Reviewer: P.B.Dubovskiĭ (Obninsk) MSC: 35B40 35L65 35Q53 PDFBibTeX XMLCite \textit{P. I. Naumkin} and \textit{I. A. Shishmarev}, Math. Notes 59, No. 6, 618--624 (1996; Zbl 0881.35016); translation from Mat. Zametki 59, No. 6, 855--864 (1996) Full Text: DOI
Naumkin, P. I.; Shishmarev, I. A. Asymptotics for \(t\to\infty\) of solutions to the generalized Korteweg-de Vries equation. (English. Russian original) Zbl 0878.35100 Dokl. Math. 52, No. 2, 193-196 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 344, No. 2, 165-167 (1995). MSC: 35Q53 35B40 PDFBibTeX XMLCite \textit{P. I. Naumkin} and \textit{I. A. Shishmarev}, Dokl. Math. 52, No. 2, 193--196 (1995; Zbl 0878.35100); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 344, No. 2, 165--167 (1995)
Naumkin, P. I.; Shishmarev, I. A. Asymptotic relationship as \(t \to \infty\) between solutions to some nonlinear equations. I. (English. Russian original) Zbl 0846.35121 Differ. Equations 30, No. 5, 806-814 (1994); translation from Differ. Uravn. 30, No. 5, 873-881 (1994). Reviewer: V.Chernyatin (Szczecin) MSC: 35Q53 35B40 PDFBibTeX XMLCite \textit{P. I. Naumkin} and \textit{I. A. Shishmarev}, Differ. Equations 30, No. 5, 806--814 (1994; Zbl 0846.35121); translation from Differ. Uravn. 30, No. 5, 873--881 (1994)
Naumkin, P. I.; Shishmarev, I. A. On the connection between the solutions of various nonlinear equations for large time. (English. Russian original) Zbl 0832.35063 Russ. Acad. Sci., Dokl., Math. 49, No. 1, 127-131 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 334, No. 4, 429-432 (1994). MSC: 35G10 35K25 35Q53 35B40 35K55 PDFBibTeX XMLCite \textit{P. I. Naumkin} and \textit{I. A. Shishmarev}, Russ. Acad. Sci., Dokl., Math. 49, No. 1, 429--432 (1994; Zbl 0832.35063); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 334, No. 4, 429--432 (1994)
Naumkin, P. I. On the asymptotics as \(t\to \infty\) of solutions of nonlinear equations in the case of maximal order. (English. Russian original) Zbl 0832.35128 Differ. Equations 29, No. 6, 926-929 (1993); translation from Differ. Uravn. 29, No. 6, 1071-1074 (1993). MSC: 35Q53 35B40 35S15 PDFBibTeX XMLCite \textit{P. I. Naumkin}, Differ. Equations 29, No. 6, 1 (1993; Zbl 0832.35128); translation from Differ. Uravn. 29, No. 6, 1071--1074 (1993)
Naumkin, P. I.; Shishmarëv, I. A. Asymptotics, as \(t\to\infty\), of the solution of a nonlinear equation with weak dissipation and dispersion. (English. Russian original) Zbl 0820.35120 Russ. Acad. Sci., Izv., Math. 43, No. 3, 443-453 (1994); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 57, No. 6, 52-63 (1993). MSC: 35Q53 35B40 76B15 PDFBibTeX XMLCite \textit{P. I. Naumkin} and \textit{I. A. Shishmarëv}, Russ. Acad. Sci., Izv., Math. 43, No. 3, 1 (1993; Zbl 0820.35120); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 57, No. 6, 52--63 (1993) Full Text: DOI
Naumkin, P. I.; Shishmarëv, I. A. Asymptotic solution for the Korteweg-de Vries equation with weak dissipation as time tends to infinity. (English. Russian original) Zbl 0798.35136 Differ. Equations 29, No. 2, 253-263 (1993); translation from Differ. Uravn. 29, No. 2, 306-319 (1993). Reviewer: A.V.Aminova (Kazan’) MSC: 35Q53 35C20 PDFBibTeX XMLCite \textit{P. I. Naumkin} and \textit{I. A. Shishmarëv}, Differ. Equations 29, No. 2, 1 (1993; Zbl 0798.35136); translation from Differ. Uravn. 29, No. 2, 306--319 (1993)
Naumkin, P. I. Solution asymptotics for nonlinear dissipative equations at large \(x\) and \(t\). (English. Russian original) Zbl 0806.35162 Mosk. Univ. Phys. Bull. 47, No. 1, 12-15 (1992); translation from Vestn. Mosk. Univ., Ser. III 33, No. 1, 12-15 (1992). Reviewer: E.Feireisl MSC: 35Q53 PDFBibTeX XMLCite \textit{P. I. Naumkin}, Mosc. Univ. Phys. Bull. 47, No. 1, 12--15 (1992; Zbl 0806.35162); translation from Vestn. Mosk. Univ., Ser. III 33, No. 1, 12--15 (1992)
Naumkin, P. I.; Shishmarev, I. A. Generalized solutions for the Whitham equation. (English. Russian original) Zbl 0788.76014 Differ. Equations 28, No. 1, 115-120 (1992); translation from Differ. Uravn. 28, No. 1, 121-126 (1992). MSC: 76B15 35Q53 35L60 35L67 PDFBibTeX XMLCite \textit{P. I. Naumkin} and \textit{I. A. Shishmarev}, Differ. Equations 28, No. 1, 115--120 (1992; Zbl 0788.76014); translation from Differ. Uravn. 28, No. 1, 121--126 (1992)
Naumkin, P. I.; Shishmarev, I. A. Generalized solutions for the Whitham equation. (Russian) Zbl 0751.76009 Differ. Uravn. 28, No. 1, 121-126 (1992). Reviewer: B.A.Malomed (Ramat Aviv) MSC: 76B15 35Q53 35L60 35L67 PDFBibTeX XMLCite \textit{P. I. Naumkin} and \textit{I. A. Shishmarev}, Differ. Uravn. 28, No. 1, 121--126 (1992; Zbl 0751.76009)
Naumkin, P. I.; Shishmarev, I. A. Asymptotic behaviour of solutions of dissipative nonlinear evolution equations for large time. (English) Zbl 0803.35130 Mathematical modelling and applied mathematics, Proc. IMACS Int. Conf., Moscow/USSR 1990, 313-322 (1992). MSC: 35Q53 35R10 35B40 PDFBibTeX XMLCite \textit{P. I. Naumkin} and \textit{I. A. Shishmarev}, in: Mathematical modelling and applied mathematics. Proceedings of the IMACS international conference, held in Moscow, USSR, June 18-23, 1990. Amsterdam etc.: North-Holland. 313--322 (1992; Zbl 0803.35130)
Naumkin, P. I.; Shishmarev, I. A. On the Cauchy problem for Whitham’s equation. (English. Russian original) Zbl 0557.45006 Sov. Math., Dokl. 28, 719-721 (1983); translation from Dokl. Akad. Nauk SSSR 273, 804-807 (1983). Reviewer: G.Cimmino MSC: 45K05 35Q99 76B15 PDFBibTeX XMLCite \textit{P. I. Naumkin} and \textit{I. A. Shishmarev}, Sov. Math., Dokl. 28, 719--721 (1983; Zbl 0557.45006); translation from Dokl. Akad. Nauk SSSR 273, 804--807 (1983)