Abstract
This paper addresses Wu–Zhang system to study dispersive long waves. The extended trial equation method extracts solitary waves, shock waves and singular solitary waves solutions. Subsequently, Lie group formalism is also applied to derive symmetries of the Wu–Zhang system and the derived ordinary differential equations are further analyzed to retrieve exact solutions are obtained. Finally, implementation of mapping method secures additional exact solutions.
Highlights
The study of nonlinear evolution equations (NLEEs) forms the basic fabric for various areas of mathematical physics and engineering
There are various forms of NLEEs that are studied for this purpose [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]
This paper will study one such NLEE that appears in dispersive long wave dynamics
Summary
The study of nonlinear evolution equations (NLEEs) forms the basic fabric for various areas of mathematical physics and engineering. This paper will study one such NLEE that appears in dispersive long wave dynamics. This is the WuZhang model [29]. Many powerful methods for obtaining the exact solutions of NLEEs have been presented in the literature [1,2,3,4, 6,7,8, 10, 11, 15, 23, 27, 28, 30]. The powerful and effective method for finding exact solutions of PDEs has been proposed by Liu and called the Liu method [17]. The mapping method has been employed to obtain periodic wave solutions in terms of Jacobi elliptic functions (JEFs) and their infinite period counterparts have been deduced [12,13,14, 16, 26]
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