Abstract
In this article, a generalized (3 + 1)-dimensional nonlinear evolution equation (NLEE), which can be obtained by a multivariate polynomial, is investigated. Based on the Hirota bilinear method, the N-soliton solution and bilinear Bäcklund transformation (BBT) with explicit formulas are successfully constructed. By using BBT, two traveling wave solutions and a mixed solution of the generalized (3 + 1)-dimensional NLEE are obtained. Furthermore, the lump and the interaction solutions for the equation are constructed. Finally, the dynamic properties of the lump and the interaction solutions are described graphically.
Highlights
With recent advancements in nonlinear science, the application of nonlinear evolution equations (NLEEs) has gained more prominence amongst mathematicians and physicists.e use of NLEEs is important because NLEEs can be used to describe many interesting nonlinear dynamic behaviors in nonlinear fields like optical fibers, plasma physics, atmospheric science, biologic nerve propagation, and marine science
E use of NLEEs is important because NLEEs can be used to describe many interesting nonlinear dynamic behaviors in nonlinear fields like optical fibers, plasma physics, atmospheric science, biologic nerve propagation, and marine science
Many effective methods for solving NLEEs have been proposed by previous researchers [1,2,3,4,5,6,7,8,9]
Summary
With recent advancements in nonlinear science, the application of nonlinear evolution equations (NLEEs) has gained more prominence amongst mathematicians and physicists. Zhang et al obtained the exact solutions for generalized nonlinear diffusion equations by using the separation of variables method [4]. He and Wu used the Exp-function method to solve the nonlinear wave equations [5]. Amongst the proposed methods [1,2,3,4,5,6,7,8,9], the Hirota bilinear method is one of the most direct and effective methods for obtaining the exact solution of the NLEEs. e most critical step in using the Hirota bilinear method is to transform the original nonlinear equation into a bilinear equation by introducing appropriate variable transformations. The Hirota bilinear equations derived from multivariable polynomials have linear subspace solutions. Their dynamical behaviors are shown under some selected values of parameters. e article is concluded with a summary and the implications of this research
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