Hong, Jin; Lai, Shaoyong The local strong solution and wave breaking feature to a Camassa-Holm type equation. (English) Zbl 1509.35263 Results Appl. Math. 17, Article ID 100358, 7 p. (2023). MSC: 35Q53 35G25 35D35 35B44 35A01 35A02 PDFBibTeX XMLCite \textit{J. Hong} and \textit{S. Lai}, Results Appl. Math. 17, Article ID 100358, 7 p. (2023; Zbl 1509.35263) Full Text: DOI
Ming, Sen; Lai, Shaoyong; Su, Yeqin The optimal control problem with necessity condition for a viscous shallow water equation. (English) Zbl 1499.49021 Bound. Value Probl. 2018, Paper No. 71, 16 p. (2018). MSC: 49J20 49K20 35Q35 35Q53 76B15 PDFBibTeX XMLCite \textit{S. Ming} et al., Bound. Value Probl. 2018, Paper No. 71, 16 p. (2018; Zbl 1499.49021) Full Text: DOI
Lai, Shaoyong; Wu, Meng Global weak solutions for a generalized Dullin-Gottwald-Holm equation in the space \(H^1(\mathbb R)\). (English) Zbl 1304.35557 Bound. Value Probl. 2014, Paper No. 203, 19 p. (2014). MSC: 35Q35 35Q51 35Q53 35D30 35A01 PDFBibTeX XMLCite \textit{S. Lai} and \textit{M. Wu}, Bound. Value Probl. 2014, Paper No. 203, 19 p. (2014; Zbl 1304.35557) Full Text: DOI
Lai, Shaoyong Global weak solutions to the Novikov equation. (English) Zbl 1283.35112 J. Funct. Anal. 265, No. 4, 520-544 (2013). MSC: 35Q53 35D30 PDFBibTeX XMLCite \textit{S. Lai}, J. Funct. Anal. 265, No. 4, 520--544 (2013; Zbl 1283.35112) Full Text: DOI
Guo, Yunxi; Lai, Shaoyong; Wu, Yonghong On existence and uniqueness of the global weak solution for a shallow water equation. (English) Zbl 1278.35214 Appl. Math. Comput. 218, No. 23, 11410-11420 (2012). MSC: 35Q53 35A01 35A02 35D30 76B03 PDFBibTeX XMLCite \textit{Y. Guo} et al., Appl. Math. Comput. 218, No. 23, 11410--11420 (2012; Zbl 1278.35214) Full Text: DOI
Sheng, Zhaowei; Lai, Shaoyong; Ma, Yuan; Luo, Xuanjun The \(H^1(\mathbb R)\) space global weak solutions to the weakly dissipative Camassa-Holm equation. (English) Zbl 1253.35154 Abstr. Appl. Anal. 2012, Article ID 693010, 21 p. (2012). MSC: 35Q53 PDFBibTeX XMLCite \textit{Z. Sheng} et al., Abstr. Appl. Anal. 2012, Article ID 693010, 21 p. (2012; Zbl 1253.35154) Full Text: DOI
Lai, Shaoyong; Xie, Qichang; Guo, Yunxi; Wu, Yonghong The existence of weak solutions for a generalized Camassa-Holm equation. (English) Zbl 1231.35206 Commun. Pure Appl. Anal. 10, No. 1, 45-57 (2011). MSC: 35Q53 35D30 35L05 PDFBibTeX XMLCite \textit{S. Lai} et al., Commun. Pure Appl. Anal. 10, No. 1, 45--57 (2011; Zbl 1231.35206) Full Text: DOI
Lai, Shaoyong The local strong and weak solutions for a nonlinear dissipative Camassa-Holm equation. (English) Zbl 1228.35204 Abstr. Appl. Anal. 2011, Article ID 285040, 15 p. (2011). MSC: 35Q53 35D30 PDFBibTeX XMLCite \textit{S. Lai}, Abstr. Appl. Anal. 2011, Article ID 285040, 15 p. (2011; Zbl 1228.35204) Full Text: DOI
Lai, Shaoyong; Wu, Yonghong A model containing both the Camassa-Holm and Degasperis-Procesi equations. (English) Zbl 1202.35231 J. Math. Anal. Appl. 374, No. 2, 458-469 (2011). MSC: 35Q53 35D30 35A01 35A02 PDFBibTeX XMLCite \textit{S. Lai} and \textit{Y. Wu}, J. Math. Anal. Appl. 374, No. 2, 458--469 (2011; Zbl 1202.35231) Full Text: DOI
Lai, Shaoyong; Wu, Yonghong Local well-posedness and weak solutions for a weakly dissipative Camassa-Holm equation. (Chinese. English summary) Zbl 1488.35485 Sci. Sin., Math. 40, No. 9, 901-920 (2010). MSC: 35Q53 35D35 35D30 PDFBibTeX XMLCite \textit{S. Lai} and \textit{Y. Wu}, Sci. Sin., Math. 40, No. 9, 901--920 (2010; Zbl 1488.35485) Full Text: DOI
Li, Nan; Yin, Zheng; Lai, Shaoyong The existence of weak solutions for a generalized Camassa-Holm equation. (English) Zbl 1219.35239 Int. Math. Forum 5, No. 41-44, 2011-2021 (2010). MSC: 35Q53 35B35 35D30 35B65 PDFBibTeX XMLCite \textit{N. Li} et al., Int. Math. Forum 5, No. 41--44, 2011--2021 (2010; Zbl 1219.35239) Full Text: Link
Li, Nan; Lv, Xiumei; Lai, Shaoyong Exact solutions to a generalized BBM equation with variable coefficients. (English) Zbl 1219.35238 Int. Math. Forum 5, No. 41-44, 2001-2009 (2010). MSC: 35Q53 35B35 35C09 35C07 35C08 PDFBibTeX XMLCite \textit{N. Li} et al., Int. Math. Forum 5, No. 41--44, 2001--2009 (2010; Zbl 1219.35238) Full Text: Link
Lv, Xiumei; Lai, Shaoyong; Wu, Yonghong The physical structures of solutions for generalized \(K(n,n)\) and \(BBM\) equations with variable coefficients. (English) Zbl 1202.35242 Math. Comput. Modelling 52, No. 5-6, 781-790 (2010). MSC: 35Q53 35A35 PDFBibTeX XMLCite \textit{X. Lv} et al., Math. Comput. Modelling 52, No. 5--6, 781--790 (2010; Zbl 1202.35242) Full Text: DOI
Guo, Yunxi; Lai, Shaoyong New exact solutions for an \((N+1)\)-dimensional generalized Boussinesq equation. (English) Zbl 1187.35210 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 6, 2863-2873 (2010). MSC: 35Q53 35-04 35R35 80A22 35C05 PDFBibTeX XMLCite \textit{Y. Guo} and \textit{S. Lai}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 6, 2863--2873 (2010; Zbl 1187.35210) Full Text: DOI
Lai, Shaoyong; Lv, Xiumei; Shuai, Mingyou The Jacobi elliptic function solutions to a generalized Benjamin-Bona-Mahony equation. (English) Zbl 1165.35447 Math. Comput. Modelling 49, No. 1-2, 369-378 (2009). MSC: 35Q53 33E05 PDFBibTeX XMLCite \textit{S. Lai} et al., Math. Comput. Modelling 49, No. 1--2, 369--378 (2009; Zbl 1165.35447) Full Text: DOI
Lai, Shaoyong Different physical structures of solutions for a generalized Boussinesq wave equation. (English) Zbl 1177.35202 J. Comput. Appl. Math. 231, No. 1, 311-318 (2009). MSC: 35Q53 35B10 35C05 35Q51 PDFBibTeX XMLCite \textit{S. Lai}, J. Comput. Appl. Math. 231, No. 1, 311--318 (2009; Zbl 1177.35202) Full Text: DOI
Zhang, Yi; Lai, Shaoyong; Yin, Jun; Wu, Yonghong The application of the auxiliary equation technique to a generalized mKdV equation with variable coefficients. (English) Zbl 1158.35422 J. Comput. Appl. Math. 223, No. 1, 75-85 (2009). MSC: 35Q53 35Q51 35C05 PDFBibTeX XMLCite \textit{Y. Zhang} et al., J. Comput. Appl. Math. 223, No. 1, 75--85 (2009; Zbl 1158.35422) Full Text: DOI
Lai, Shaoyong; Wu, Yonghong; Zhou, Yuan Some physical structures for the \((2+1)\)-dimensional Boussinesq water equation with positive and negative exponents. (English) Zbl 1155.76310 Comput. Math. Appl. 56, No. 2, 339-345 (2008). MSC: 76B15 35Q53 PDFBibTeX XMLCite \textit{S. Lai} et al., Comput. Math. Appl. 56, No. 2, 339--345 (2008; Zbl 1155.76310) Full Text: DOI
Lai, Shaoyong; Wu, Y. H.; Wiwatanapataphee, B. On exact travelling wave solutions for two types of nonlinear \(K(n,n)\) equations and a generalized KP equation. (English) Zbl 1187.35216 J. Comput. Appl. Math. 212, No. 2, 291-299 (2008). Reviewer: Pavel Burda (Praha) MSC: 35Q53 35Q51 35B10 PDFBibTeX XMLCite \textit{S. Lai} et al., J. Comput. Appl. Math. 212, No. 2, 291--299 (2008; Zbl 1187.35216) Full Text: DOI
Liu, Shihuan; Zhong, Yue; Huang, Wenyi; Lai, Shaoyong The global solution of a damped Boussinesq equation with initial boundary conditions. (Chinese. English summary) Zbl 1150.35553 J. Sichuan Norm. Univ., Nat. Sci. 30, No. 3, 275-279 (2007). MSC: 35Q53 35L05 PDFBibTeX XMLCite \textit{S. Liu} et al., J. Sichuan Norm. Univ., Nat. Sci. 30, No. 3, 275--279 (2007; Zbl 1150.35553)
Cai, Hongmei; Lai, Shaoyong The asymptotics of solutions for a generalized Boussinesq water system in two-dimensional space. (English) Zbl 1125.35079 Math. Appl. 20, No. 1, 151-157 (2007). MSC: 35Q53 PDFBibTeX XMLCite \textit{H. Cai} and \textit{S. Lai}, Math. Appl. 20, No. 1, 151--157 (2007; Zbl 1125.35079)
Lai, Shao Yong; Wu, Yong Hong; Zhang, Guangquan The global solution of an initial value problem for a generalized Boussinesq equation. (English) Zbl 1050.35087 Int. J. Differ. Equ. Appl. 7, No. 2, 153-163 (2003). Reviewer: Bruno Scarpellini (Basel) MSC: 35Q35 35Q53 76B03 PDFBibTeX XMLCite \textit{S. Y. Lai} et al., Int. J. Differ. Equ. Appl. 7, No. 2, 153--163 (2003; Zbl 1050.35087)