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Wang, Xiaoli; Wu, Zekang; Han, Wenjing; Yan, Zhenya Deep learning data-driven multi-soliton dynamics and parameters discovery for the fifth-order Kaup-Kuperschmidt equation. (English) Zbl 07736392 Physica D 454, Article ID 133862, 18 p. (2023). MSC: 68-XX 92-XX PDFBibTeX XMLCite \textit{X. Wang} et al., Physica D 454, Article ID 133862, 18 p. (2023; Zbl 07736392) Full Text: DOI
Manoranjan, Valipuram; Alzaleq, Lewa’ Analysis of a population model with advection and an autocatalytic-type growth. (English) Zbl 1505.92166 Int. J. Biomath. 16, No. 2, Article ID 2250078, 21 p. (2023). MSC: 92D25 35C07 65M06 PDFBibTeX XMLCite \textit{V. Manoranjan} and \textit{L. Alzaleq}, Int. J. Biomath. 16, No. 2, Article ID 2250078, 21 p. (2023; Zbl 1505.92166) Full Text: DOI
Jadaun, Vishakha Pulsatile blood flow in healthy aorta: an application of nonlinear evolution equation. (English) Zbl 1498.92072 Int. J. Biomath. 15, No. 7, Article ID 2250047, 30 p. (2022). MSC: 92C35 47J35 35Q51 PDFBibTeX XMLCite \textit{V. Jadaun}, Int. J. Biomath. 15, No. 7, Article ID 2250047, 30 p. (2022; Zbl 1498.92072) Full Text: DOI
McCue, Scott W.; Bradshaw-Hajek, Bronwyn H.; Simpson, Matthew J. Exact time-dependent solutions of a Fisher-KPP-like equation obtained with nonclassical symmetry analysis. (English) Zbl 1491.35100 Appl. Math. Lett. 132, Article ID 108151, 8 p. (2022). MSC: 35C05 35C06 35K57 92D25 PDFBibTeX XMLCite \textit{S. W. McCue} et al., Appl. Math. Lett. 132, Article ID 108151, 8 p. (2022; Zbl 1491.35100) Full Text: DOI arXiv
Jadaun, Vishakha; Singh, Nitin Raja; Singh, Shveta; Shankar, Ravi Impact of solitons on the progression of initial lesion in aortic dissection. (English) Zbl 1492.92017 Int. J. Biomath. 15, No. 3, Article ID 2150096, 24 p. (2022). MSC: 92C32 92C35 35C08 47J35 PDFBibTeX XMLCite \textit{V. Jadaun} et al., Int. J. Biomath. 15, No. 3, Article ID 2150096, 24 p. (2022; Zbl 1492.92017) Full Text: DOI
Tabi, C. B.; Etémé, A. S.; Mohamadou, A.; Kofané, T. C. Oscillating two-dimensional \(\mathrm{Ca}^{2+}\) waves in cell networks with bidirectional paracrine signaling. (English) Zbl 1496.92016 Waves Random Complex Media 31, No. 6, 1028-1050 (2021). MSC: 92C37 92C42 PDFBibTeX XMLCite \textit{C. B. Tabi} et al., Waves Random Complex Media 31, No. 6, 1028--1050 (2021; Zbl 1496.92016) Full Text: DOI
Chulián, Salvador; Martinez-Rubio, Álvaro; Gandarias, María Luz; Rosa, María Lie point symmetries for generalised Fisher’s equations describing tumour dynamics. (English) Zbl 1471.92093 Math. Biosci. Eng. 18, No. 4, 3291-3312 (2021). MSC: 92C32 35Q92 PDFBibTeX XMLCite \textit{S. Chulián} et al., Math. Biosci. Eng. 18, No. 4, 3291--3312 (2021; Zbl 1471.92093) Full Text: DOI
Levi, Decio; Rodríguez, Miguel A.; Thomova, Zora Conditional discretization of a generalized reaction-diffusion equation. (English) Zbl 1498.65186 Paranjape, M. B. (ed.) et al., Quantum theory and symmetries. Proceedings of the 11th international symposium, Montréal, Canada, July 1–5, 2019. Cham: Springer. CRM Ser. Math. Phys., 149-156 (2021). Reviewer: Murli Gupta (Washington, D.C.) MSC: 65M99 22E70 35K57 37K10 92C20 35Q92 PDFBibTeX XMLCite \textit{D. Levi} et al., in: Quantum theory and symmetries. Proceedings of the 11th international symposium, Montréal, Canada, July 1--5, 2019. Cham: Springer. 149--156 (2021; Zbl 1498.65186) Full Text: DOI
Khan, Hassan; Shah, Rasool; Gómez-Aguilar, J. F.; Shoaib; Baleanu, Dumitru; Kumam, Poom Travelling waves solution for fractional-order biological population model. (English) Zbl 1469.92094 Math. Model. Nat. Phenom. 16, Paper No. 32, 24 p. (2021). MSC: 92D25 35C07 35R11 PDFBibTeX XMLCite \textit{H. Khan} et al., Math. Model. Nat. Phenom. 16, Paper No. 32, 24 p. (2021; Zbl 1469.92094) Full Text: DOI
Cherniha, Roman; Serov, Mykola; Pliukhin, Oleksii Lie and \(Q\)-conditional symmetries of reaction-diffusion-convection equations with exponential nonlinearities and their application for finding exact solutions. (English) Zbl 1423.35195 Symmetry 10, No. 4, Paper No. 123, 33 p. (2018). MSC: 35K57 35K55 35C05 92D25 PDFBibTeX XMLCite \textit{R. Cherniha} et al., Symmetry 10, No. 4, Paper No. 123, 33 p. (2018; Zbl 1423.35195) Full Text: DOI
Rosa, M.; Camacho, J. C.; Bruzón, M. S.; Gandarias, M. L. Classical and potential symmetries for a generalized Fisher equation. (English) Zbl 1355.76054 J. Comput. Appl. Math. 318, 181-188 (2017). MSC: 76M60 92D25 35Q91 PDFBibTeX XMLCite \textit{M. Rosa} et al., J. Comput. Appl. Math. 318, 181--188 (2017; Zbl 1355.76054) Full Text: DOI
Broadbridge, P.; Bradshaw-Hajek, B. H. Exact solutions for logistic reaction-diffusion equations in biology. (English) Zbl 1365.35067 Z. Angew. Math. Phys. 67, No. 4, Article ID 93, 13 p. (2016). MSC: 35K57 35K55 92D25 92D99 35C05 PDFBibTeX XMLCite \textit{P. Broadbridge} and \textit{B. H. Bradshaw-Hajek}, Z. Angew. Math. Phys. 67, No. 4, Article ID 93, 13 p. (2016; Zbl 1365.35067) Full Text: DOI arXiv
Bracken, A. J.; Bass, L. Differential equations of electrodiffusion: constant field solutions, uniqueness, and new formulas of Goldman-Hodgkin-Katz type. (English) Zbl 1404.82055 SIAM J. Appl. Math. 76, No. 6, 2286-2305 (2016). MSC: 82C70 82D15 92B05 34B05 34B15 PDFBibTeX XMLCite \textit{A. J. Bracken} and \textit{L. Bass}, SIAM J. Appl. Math. 76, No. 6, 2286--2305 (2016; Zbl 1404.82055) Full Text: DOI arXiv
Morgan, C. E.; Breward, C. J. W.; Griffiths, I. M.; Howell, P. D. Mathematical modelling of surfactant self-assembly at interfaces. (English) Zbl 1319.35282 SIAM J. Appl. Math. 75, No. 2, 836-860 (2015). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q99 35R37 92E99 PDFBibTeX XMLCite \textit{C. E. Morgan} et al., SIAM J. Appl. Math. 75, No. 2, 836--860 (2015; Zbl 1319.35282) Full Text: DOI Link
Solis, Francisco J.; Ku-Carrillo, Roberto A. Generic predation in age structure predator-prey models. (English) Zbl 1410.92110 Appl. Math. Comput. 231, 205-213 (2014). MSC: 92D25 PDFBibTeX XMLCite \textit{F. J. Solis} and \textit{R. A. Ku-Carrillo}, Appl. Math. Comput. 231, 205--213 (2014; Zbl 1410.92110) Full Text: DOI
Cherniha, Roman; Pliukhin, Oleksii New conditional symmetries and exact solutions of reaction-diffusion-convection equations with exponential nonlinearities. (English) Zbl 1286.35012 J. Math. Anal. Appl. 403, No. 1, 23-37 (2013). MSC: 35B06 35K57 35K58 35C05 92D25 35K20 PDFBibTeX XMLCite \textit{R. Cherniha} and \textit{O. Pliukhin}, J. Math. Anal. Appl. 403, No. 1, 23--37 (2013; Zbl 1286.35012) Full Text: DOI
Cherniha, Roman; Davydovych, Vasyl’ Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system. (English) Zbl 1228.35120 Math. Comput. Modelling 54, No. 5-6, 1238-1251 (2011). MSC: 35K57 35Q92 35B06 35C05 92D25 PDFBibTeX XMLCite \textit{R. Cherniha} and \textit{V. Davydovych}, Math. Comput. Modelling 54, No. 5--6, 1238--1251 (2011; Zbl 1228.35120) Full Text: DOI arXiv
Derks, Gianne; Gaeta, Giuseppe A minimal model of DNA dynamics in interaction with RNA-polymerase. (English) Zbl 1227.92021 Physica D 240, No. 22, 1805-1817 (2011). MSC: 92C40 37N25 PDFBibTeX XMLCite \textit{G. Derks} and \textit{G. Gaeta}, Physica D 240, No. 22, 1805--1817 (2011; Zbl 1227.92021) Full Text: DOI Link
Vitanov, Nikolay K.; Dimitrova, Zlatinka I. Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics. (English) Zbl 1222.35201 Commun. Nonlinear Sci. Numer. Simul. 15, No. 10, 2836-2845 (2010). MSC: 35Q92 35C07 92D25 92D40 35K57 PDFBibTeX XMLCite \textit{N. K. Vitanov} and \textit{Z. I. Dimitrova}, Commun. Nonlinear Sci. Numer. Simul. 15, No. 10, 2836--2845 (2010; Zbl 1222.35201) Full Text: DOI
Chen, Guowang; Guo, Hongxia; Zhang, Hongwei Global existence of solutions of Cauchy problem for generalized system of nonlinear evolution equations arising from DNA. (English) Zbl 1298.35229 J. Math. Phys. 50, No. 8, 083514, 23 p. (2009). MSC: 35Q92 92D10 PDFBibTeX XMLCite \textit{G. Chen} et al., J. Math. Phys. 50, No. 8, 083514, 23 p. (2009; Zbl 1298.35229) Full Text: DOI
Vitanov, Nikolay K.; Jordanov, Ivan P.; Dimitrova, Zlatinka I. On nonlinear population waves. (English) Zbl 1181.92083 Appl. Math. Comput. 215, No. 8, 2950-2964 (2009). MSC: 92D40 35Q92 35B35 PDFBibTeX XMLCite \textit{N. K. Vitanov} et al., Appl. Math. Comput. 215, No. 8, 2950--2964 (2009; Zbl 1181.92083) Full Text: DOI
Browne, P.; Momoniat, E.; Mahomed, F. M. A generalized FitzHugh-Nagumo equation. (English) Zbl 1135.35009 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 4, 1006-1015 (2008). Reviewer: Werner M. Seiler (Kassel) MSC: 35A30 92C20 35C05 35K57 65M20 58J72 58J70 PDFBibTeX XMLCite \textit{P. Browne} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 4, 1006--1015 (2008; Zbl 1135.35009) Full Text: DOI
Sinkala, Zachariah Soliton/exciton transport in proteins. (English) Zbl 1441.92017 J. Theor. Biol. 241, No. 4, 919-927 (2006). MSC: 92C40 PDFBibTeX XMLCite \textit{Z. Sinkala}, J. Theor. Biol. 241, No. 4, 919--927 (2006; Zbl 1441.92017) Full Text: DOI Link
Shih, M.; Momoniat, E.; Mahomed, F. M. Approximate conditional symmetries and approximate solutions of the perturbed Fitzhugh-Nagumo equation. (English) Zbl 1076.35052 J. Math. Phys. 46, No. 2, 023503, 10 p. (2005). MSC: 35K55 35A30 92C20 PDFBibTeX XMLCite \textit{M. Shih} et al., J. Math. Phys. 46, No. 2, 023503, 10 p. (2005; Zbl 1076.35052) Full Text: DOI
Bradshaw-Hajek, B. H.; Broadbridge, P. A robust cubic reaction-diffusion system for gene propagation. (English) Zbl 1065.92030 Math. Comput. Modelling 39, No. 9-10, 1151-1163 (2004). MSC: 92D10 35K57 92D15 35Q92 PDFBibTeX XMLCite \textit{B. H. Bradshaw-Hajek} and \textit{P. Broadbridge}, Math. Comput. Modelling 39, No. 9--10, 1151--1163 (2004; Zbl 1065.92030) Full Text: DOI
Hu, X. B.; Clarkson, P. A. Rational solutions of an extended Lotka-Volterra equation. (English) Zbl 1362.34099 J. Nonlinear Math. Phys. 9, Suppl. 1, 75-86 (2002). MSC: 34K06 34C20 37N25 92D25 37K35 PDFBibTeX XMLCite \textit{X. B. Hu} and \textit{P. A. Clarkson}, J. Nonlinear Math. Phys. 9, 75--86 (2002; Zbl 1362.34099) Full Text: DOI
Broadbridge, P.; Bradshaw, B. H.; Fulford, G. R.; Aldis, G. K. Huxley and Fisher equations for gene propagation: an exact solution. (English) Zbl 1043.35041 ANZIAM J. 44, No. 1, 11-20 (2002). MSC: 35C05 92D25 35K57 PDFBibTeX XMLCite \textit{P. Broadbridge} et al., ANZIAM J. 44, No. 1, 11--20 (2002; Zbl 1043.35041) Full Text: DOI
Daniel, M.; Latha, M. M. A generalized Davydov soliton model for energy transfer in alpha helical proteins. (English) Zbl 0971.92014 Physica A 298, No. 3-4, 351-370 (2001). MSC: 92C40 92C05 35Q51 PDFBibTeX XMLCite \textit{M. Daniel} and \textit{M. M. Latha}, Physica A 298, No. 3--4, 351--370 (2001; Zbl 0971.92014) Full Text: DOI
Nucci, M. C. The role of symmetries in solving differential equations. (English) Zbl 0884.76075 Math. Comput. Modelling 25, No. 8-9, 181-193 (1997). MSC: 76M99 76S05 35A30 92D30 PDFBibTeX XMLCite \textit{M. C. Nucci}, Math. Comput. Modelling 25, No. 8--9, 181--193 (1997; Zbl 0884.76075) Full Text: DOI
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