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Volume 32, Issue 2
Traveling Wave Solutions and Their Stability of Nonlinear Schrödinger Equation with Weak Dissipation

Yancong Xu, Tianzhu Lan & Yongli Liu

Ann. Appl. Math., 32 (2016), pp. 183-199.

Published online: 2022-06

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  • Abstract

In this paper, several new constant-amplitude and variable-amplitude wave solutions (namely, traveling wave solutions) of a generalized nonlinear Schrödinger equation are investigated by using the extended homogeneous balance method, where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. In addition, stability analysis of those solutions are also conducted by regular phase plane technique.

  • Keywords

nonlinear Schrödinger equation, extended homogeneous balance method, amplitude wave solutions, stability.

  • AMS Subject Headings

35B40, 35K58, 35B32

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-32-183, author = {Xu , YancongLan , Tianzhu and Liu , Yongli}, title = {Traveling Wave Solutions and Their Stability of Nonlinear Schrödinger Equation with Weak Dissipation}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {32}, number = {2}, pages = {183--199}, abstract = {

In this paper, several new constant-amplitude and variable-amplitude wave solutions (namely, traveling wave solutions) of a generalized nonlinear Schrödinger equation are investigated by using the extended homogeneous balance method, where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. In addition, stability analysis of those solutions are also conducted by regular phase plane technique.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20637.html} }
TY - JOUR T1 - Traveling Wave Solutions and Their Stability of Nonlinear Schrödinger Equation with Weak Dissipation AU - Xu , Yancong AU - Lan , Tianzhu AU - Liu , Yongli JO - Annals of Applied Mathematics VL - 2 SP - 183 EP - 199 PY - 2022 DA - 2022/06 SN - 32 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/aam/20637.html KW - nonlinear Schrödinger equation, extended homogeneous balance method, amplitude wave solutions, stability. AB -

In this paper, several new constant-amplitude and variable-amplitude wave solutions (namely, traveling wave solutions) of a generalized nonlinear Schrödinger equation are investigated by using the extended homogeneous balance method, where the balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. In addition, stability analysis of those solutions are also conducted by regular phase plane technique.

Xu , YancongLan , Tianzhu and Liu , Yongli. (2022). Traveling Wave Solutions and Their Stability of Nonlinear Schrödinger Equation with Weak Dissipation. Annals of Applied Mathematics. 32 (2). 183-199. doi:
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