Abstract
In this work, the coupled nonlinear Fokas–Liu system which is a special type of KdV equation is studied using the invariant subspace method (ISM). The method determines an invariant subspace and construct the exact solutions of the nonlinear partial differential equations (NPDEs) by reducing them to ordinary differential equations (ODEs). As a result of the calculations, polynomial and logarithmic function solutions of the equation are derived. Further more, the ansatz approached is utilized to derive the topological, non-topological and other singular soliton solutions of the system. Numerical simulation off the obtained results are shown.
Highlights
nonlinear partial differential equations (NPDEs) are commonly applied to describe a lot of relevant dynamic processes and phenomena in mechanics, biology, physics, chemistry, etc
The invariant subspace method (ISM), proposed in Galaktionov [2] and modified in Ma [3], is one of strongest techniques to derive the solutions of NPDEs
The technique involve several invariant subspaces which are defined as subspaces of solutions to linear ordinary differential equations (ODEs) have been utilized to solve special NPDEs [3]
Summary
NPDEs are commonly applied to describe a lot of relevant dynamic processes and phenomena in mechanics, biology, physics, chemistry, etc. [1]. The ISM, proposed in Galaktionov [2] and modified in Ma [3], is one of strongest techniques to derive the solutions of NPDEs. The technique involve several invariant subspaces which are defined as subspaces of solutions to linear ODEs have been utilized to solve special NPDEs [3]. The ansatz technique is a powerful technique used in deriving the soliton solutions of NPDEs. The approach is based upon substituting an ansatz directly into the equation. In the last few decades, several powerful integration approaches have utilized to study many equations [11,12,13,14,15,16,17,18,19]. We will classify the soliton solutions of the equation by utilizing the the powerful ansatz approach [7, 8]
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