Abstract
With the aid of Mathematica, new exact travelling wave solutions for fifth-order KdV equation are obtained by using the solitary wave ansatz method and the Wu elimination method. The derivation of conservation laws for a fifth-order KdV equation is considered.
Highlights
It is well-known that nonlinear complex physical phenomena are related to nonlinear partial differential equations (NLPDEs) which are involved in many fields from physics to biology, chemistry, mechanics, etc
The notion of conservation laws is important in the study of nonlinear evolution equations (NLEEs) appearing in mathematical physics [19]
Problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state
Summary
It is well-known that nonlinear complex physical phenomena are related to nonlinear partial differential equations (NLPDEs) which are involved in many fields from physics to biology, chemistry, mechanics, etc. As mathematical models of the phenomena, the investigation of exact solutions to the NLPDEs reveals to be very important for the understanding of these physical problems. The notion of conservation laws is important in the study of nonlinear evolution equations (NLEEs) appearing in mathematical physics [19]. The investigation of conservation laws of the Korteweg-de Vries (KdV) equation led to the discovery of a number of techniques to solve NLEEs [21], e.g., Miura transformation, Lax pair, inverse scattering technique and bi-Hamiltonian structures. We can derive constants of motion from conservation law, which enjoys the general form as [24]. While the components V and G of the conserved vector V ,G are functions of x,t and derivatives of u. It has already been proved that a large number of NLEEs possess an infinite
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