Volume 8, Issue 6
Bifurcations and Single Peak Solitary Wave Solutions of an Integrable Nonlinear Wave Equation

Adv. Appl. Math. Mech., 8 (2016), pp. 1084-1098.

Published online: 2018-05

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• Abstract

Dynamical system theory is applied to the integrable nonlinear wave equation $u_t±(u^3−u^2)x+(u^3)xxx=0$. We obtain the single peak solitary wave solutions and compacton solutions of the equation. Regular compacton solution of the equation corresponds to the case of wave speed $c$=0. In the case of $c^6$≠0, we find smooth soliton solutions. The influence of parameters of the traveling wave solutions is explored by using the phase portrait analytical technique. Asymptotic analysis and numerical simulations are provided for these soliton solutions of the nonlinear wave equation.

• Keywords

Bifurcation, solitary wave, compaction.

35Q51, 35Q53

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@Article{AAMM-8-1084, author = {Wei and Wang and and 19605 and and Wei Wang and Chunhai and Li and and 19606 and and Chunhai Li and Wenjing and Zhu and and 19607 and and Wenjing Zhu}, title = {Bifurcations and Single Peak Solitary Wave Solutions of an Integrable Nonlinear Wave Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {6}, pages = {1084--1098}, abstract = {

Dynamical system theory is applied to the integrable nonlinear wave equation $u_t±(u^3−u^2)x+(u^3)xxx=0$. We obtain the single peak solitary wave solutions and compacton solutions of the equation. Regular compacton solution of the equation corresponds to the case of wave speed $c$=0. In the case of $c^6$≠0, we find smooth soliton solutions. The influence of parameters of the traveling wave solutions is explored by using the phase portrait analytical technique. Asymptotic analysis and numerical simulations are provided for these soliton solutions of the nonlinear wave equation.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1248}, url = {http://global-sci.org/intro/article_detail/aamm/12133.html} }
TY - JOUR T1 - Bifurcations and Single Peak Solitary Wave Solutions of an Integrable Nonlinear Wave Equation AU - Wang , Wei AU - Li , Chunhai AU - Zhu , Wenjing JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1084 EP - 1098 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2015.m1248 UR - https://global-sci.org/intro/article_detail/aamm/12133.html KW - Bifurcation, solitary wave, compaction. AB -

Dynamical system theory is applied to the integrable nonlinear wave equation $u_t±(u^3−u^2)x+(u^3)xxx=0$. We obtain the single peak solitary wave solutions and compacton solutions of the equation. Regular compacton solution of the equation corresponds to the case of wave speed $c$=0. In the case of $c^6$≠0, we find smooth soliton solutions. The influence of parameters of the traveling wave solutions is explored by using the phase portrait analytical technique. Asymptotic analysis and numerical simulations are provided for these soliton solutions of the nonlinear wave equation.

Wei Wang, Chunhai Li & Wenjing Zhu. (2020). Bifurcations and Single Peak Solitary Wave Solutions of an Integrable Nonlinear Wave Equation. Advances in Applied Mathematics and Mechanics. 8 (6). 1084-1098. doi:10.4208/aamm.2015.m1248
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