scholarly journals Numerical Estimation of Traveling Wave Solution of Two-Dimensional K-dV Equation Using a New Auxiliary Equation Method

2013 ◽  
Vol 03 (01) ◽  
pp. 27-36
Author(s):  
Rezaul Karim ◽  
Abdul Alim ◽  
Laek Sazzad Andallah
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solution ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Two Dimensional ◽  
Numerical Estimation ◽  
Auxiliary Equation Method

scholarly journals Variable Coefficient Exact Solutions for Some Nonlinear Conformable Partial Differential Equations Using an Auxiliary Equation Method

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 31
Author(s):  
Sekson Sirisubtawee ◽  
Nuntapon Thamareerat ◽  
Thitthita Iatkliang
Keyword(s):  
Partial Differential Equations ◽  
Solitary Wave ◽  
Differential Equations ◽  
Exact Solutions ◽  
Wave Solution ◽  
Variable Coefficient ◽  
Solitary Wave Solution ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Auxiliary Equation Method

The objective of this present paper is to utilize an auxiliary equation method for constructing exact solutions associated with variable coefficient function forms for certain nonlinear partial differential equations (NPDEs) in the sense of the conformable derivative. Utilizing the specific fractional transformations, the conformable derivatives appearing in the original equation can be converted into integer order derivatives with respect to new variables. As for applications of the method, we particularly obtain variable coefficient exact solutions for the conformable time (2 + 1)-dimensional Kadomtsev–Petviashvili equation and the conformable space-time (2 + 1)-dimensional Boussinesq equation. As a result, the obtained exact solutions for the equations are solitary wave solutions including a soliton solitary wave solution and a bell-shaped solitary wave solution. The advantage of the used method beyond other existing methods is that it provides variable coefficient exact solutions covering constant coefficient ones. In consequence, the auxiliary equation method based on setting all coefficients of an exact solution as variable function forms can be more extensively used, straightforward and trustworthy for solving the conformable NPDEs.

scholarly journals Single peaked traveling wave solutions to a generalized μ-Novikov Equation

2020 ◽  
Vol 10 (1) ◽  
pp. 66-75
Author(s):  
Byungsoo Moon
Keyword(s):  
Linear Combination ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Solutions ◽  
Quadratic Nonlinearities ◽  
Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

Periodic traveling-wave solution of the Sakuma-Nishiguchi equation

1996 ◽  
Vol 54 (19) ◽  
pp. 13484-13486 ◽  
Author(s):  
David R. Rowland ◽  
Zlatko Jovanoski
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solution ◽  
Periodic Traveling Wave

Simulation of bright–dark soliton solutions of the Lonngren wave equation arising the model of transmission lines

2021 ◽  
pp. 2150484
Author(s):  
Asif Yokuş
Keyword(s):  
Wave Equation ◽  
Soliton Solutions ◽  
Stationary Wave ◽  
Dark Soliton ◽  
Traveling Wave Solution ◽  
Bright Soliton ◽  
Auxiliary Equation ◽  
Discussion Section ◽  
Auxiliary Equation Method ◽  
Advantages And Disadvantages

In this study, the auxiliary equation method is applied successfully to the Lonngren wave equation. Bright soliton, bright–dark soliton solutions are produced, which play an important role in the distribution and distribution of electric charge. In the conclusion and discussion section, the effect of nonlinearity term on wave behavior in bright soliton traveling wave solution is examined. The advantages and disadvantages of the method are discussed. While graphs representing the stationary wave are obtained, special values are given to the constants in the solutions. These graphs are presented as 3D, 2D and contour.

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