scholarly journals Abundant new exact solutions to the fractional nonlinear evolution equation via Riemann-Liouville derivative

2021 ◽  
Vol 60 (6) ◽  
pp. 5183-5191
Author(s):  
M. Hafiz Uddin ◽  
M. Ayesha Khatun ◽  
Mohammad Asif Arefin ◽  
M. Ali Akbar
Keyword(s):  
Evolution Equation ◽  
Exact Solutions ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
New Exact Solutions ◽  
Liouville Derivative

scholarly journals Lie symmetry analysis, optimal system, and new exact solutions of a (3 + 1) dimensional nonlinear evolution equation

2021 ◽  
Vol 10 (1) ◽  
pp. 132-145
Author(s):  
Ashish Tiwari ◽  
Kajal Sharma ◽  
Rajan Arora
Keyword(s):  
Evolution Equation ◽  
Exact Solutions ◽  
Optical Fibers ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Similarity Solutions ◽  
Optimal System ◽  
Similarity Reduction ◽  
Evolutionary Equations ◽  
New Exact Solutions

Abstract Studies on Non-linear evolutionary equations have become more critical as time evolves. Such equations are not far-fetched in fluid mechanics, plasma physics, optical fibers, and other scientific applications. It should be an essential aim to find exact solutions of these equations. In this work, the Lie group theory is used to apply the similarity reduction and to find some exact solutions of a (3+1) dimensional nonlinear evolution equation. In this report, the groups of symmetries, Tables for commutation, and adjoints with infinitesimal generators were established. The subalgebra and its optimal system is obtained with the aid of the adjoint Table. Moreover, the equation has been reduced into a new PDE having less number of independent variables and at last into an ODE, using subalgebras and their optimal system, which gives similarity solutions that can represent the dynamics of nonlinear waves.

POSITON, NEGATON, SOLITON AND COMPLEXITON SOLUTIONS TO A FOUR-DIMENSIONAL NONLINEAR EVOLUTION EQUATION

2009 ◽  
Vol 23 (25) ◽  
pp. 2971-2991 ◽  
Author(s):  
ZHAQILAO ◽  
ZHI-BIN LI
Keyword(s):  
Evolution Equation ◽  
Exact Solutions ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Comprehensive Approach ◽  
Wronskian Determinant ◽  
Interaction Solutions ◽  
Complexiton Solutions

A generalized Wronskian formulation is presented for a four-dimensional nonlinear evolution equation. The representative systems are explicitly solved by selecting a broad set of sufficient conditions which make the Wronskian determinant a solution to the bilinearized four-dimensional nonlinear evolution equation. The obtained solution formulas provide us with a comprehensive approach to construct explicit exact solutions to the four-dimensional nonlinear evolution equation, by which positons, negatons, solitons and complexitons are computed for the four-dimensional nonlinear evolution equation. Applying the Hirota's direct method, multi-soliton, non-singular complexiton, and their interaction solutions of the four-dimensional nonlinear evolution equation are also obtained.

scholarly journals Solving nonlinear evolution equation system using two different methods

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Melike Kaplan ◽  
Ahmet Bekir ◽  
Mehmet N. Ozer
Keyword(s):  
Partial Differential Equations ◽  
Evolution Equation ◽  
Exact Solutions ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Applied Mathematics ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Equation System ◽  
Free Parameters

AbstractThis paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

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