scholarly journals The Multisoliton Solutions for the (2+1)-Dimensional Sawada-Kotera Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Zhenhui Xu ◽  
Hanlin Chen ◽  
Wei Chen
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
High Dimensional ◽  
Wave Solutions ◽  
Solitary Solutions ◽  
Ansatz Approach ◽  
Multisoliton Solutions

Applying bilinear form and extended three-wavetype of ansätz approach on the (2+1)-dimensional Sawada-Kotera equation, we obtain new multisoliton solutions, including the double periodic-type three-wave solutions, the breather two-soliton solutions, the double breather soliton solutions, and the three-solitary solutions. These results show that the high-dimensional nonlinear evolution equation has rich dynamical behavior.

New (3+1)-dimensional nonlinear evolution equation: multiple soliton solutions

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Multiple Soliton Solutions ◽  
Simplified Hirota’S Method ◽  
Hirota's Method

AbstractIn this work, we introduce an extended (3+1)-dimensional nonlinear evolution equation. We determine multiple soliton solutions by using the simplified Hirota’s method. In addition, we establish a variety of travelling wave solutions by using hyperbolic and trigonometric ansatze.

scholarly journals Lump Solutions, Multi Lump Solutions and More Soliton Solutions of a Novel (2+1)-dimensional Nonlinear Evolution Equation

2021 ◽  
Author(s):  
Hongcai Ma ◽  
Shupan Yue ◽  
Yidan Gao ◽  
Aiping Deng
Keyword(s):  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Bilinear Method ◽  
Test Function ◽  
Lump Solutions ◽  
Hirota Bilinear ◽  
Test Function Method

Abstract Exact solutions of a new (2+1)-dimensional nonlinear evolution equation are studied. Through the Hirota bilinear method, the test function method and the improved tanh-coth and tah-cot method, with the assisstance of symbolic operations, one can obtain the lump solutions, multi lump solutions and more soliton solutions. Finally, by determining different parameters, we draw the three-dimensional plots and density plots at different times.

Traveling wave solutions and conservation laws of a generalized Kudryashov–Sinelshchikov equation

2019 ◽  
Vol 25 (2) ◽  
pp. 211-217 ◽  
Author(s):  
Ben Muatjetjeja ◽  
Abdullahi Rashid Adem ◽  
Sivenathi Oscar Mbusi
Keyword(s):  
Heat Transfer ◽  
Evolution Equation ◽  
Conservation Laws ◽  
Traveling Wave ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Pressure Waves ◽  
Wave Solutions ◽  
Kudryashov Method

Abstract Kudryashov and Sinelshchikov proposed a nonlinear evolution equation that models the pressure waves in a mixture of liquid and gas bubbles by taking into account the viscosity of the liquid and the heat transfer. Conservation laws and exact solutions are computed for this underlying equation. In the analysis of this particular equation, two approaches are employed, namely, the multiplier method and Kudryashov method.

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