scholarly journals Solitary wave solutions of GKP equation with (2+1)dimensional variable-coefficients in dynamic systems

2021 ◽  
pp. 100069
Author(s):  
Zhen ZHAO ◽  
Jing PANG
Keyword(s):  
Solitary Wave ◽  
Dynamic Systems ◽  
Variable Coefficients ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Dimensional Variable

OPTICAL SOLITARY WAVES FOR THE GENERALIZED HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION WITH VARIABLE COEFFICIENTS

2007 ◽  
Vol 21 (17) ◽  
pp. 2951-2964 ◽  
Author(s):  
CHAO-QING DAI ◽  
GUO-QUAN ZHOU ◽  
JIE-FANG ZHANG
Keyword(s):  
Solitary Wave ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Solitary Waves ◽  
Schrodinger Equation ◽  
Variable Coefficients ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

In this paper, four kinds of optical solitary wave solutions, including bright, dark optical solitary waves and new types of solitary waves (W-shaped and M-shaped), for the generalized higher-order nonlinear Schrödinger equation (GHONLSE) with variable coefficients are considered under certain parametric conditions. Among these solutions, the W-shaped and M-shaped solitary waves, which cannot exist in the variable-coefficient nonlinear Schrödinger equation (vNLSE), are first given for the GHONLSE with variable coefficients. As examples, we analyze the properties of these solitary wave solutions in some periodic distributed amplification systems. When α1(z)=0, these bright and dark optical solitary wave solutions agree with the corresponding solutions in Refs. 25, 26 and 27, and the W-shaped solitary wave is in agreement with the corresponding result in Ref. 29. When α3(z)–α7(z) are constants and α1(z)=α2(z)=0, the W-shaped and M-shaped solitary waves in Refs. 14 and 15 can be recovered, respectively. Under the absence of the higher-order terms (α4(z), α6(z), α7(z)) and α1(z)=0, we provide the same results as reported in Refs. 22 and 23. This means that our results have more general forms than the earlier reports.

scholarly journals Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 896-909 ◽  
Author(s):  
Dianchen Lu ◽  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Solitary Wave ◽  
Nonlinear Partial Differential Equations ◽  
Research Work ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Mapping Method ◽  
New Method ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

AbstractIn this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

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