A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...

A computational framework for the construction of solutions to linear homogenous partial differential equations (PDEs) with variable coefficients is developed in this paper. The considered class PDEs reads: ∂p∂t−∑j=0m∑r=0njajrtxr∂jp∂xj=0 F-operators are introduced and used transform original PDE into image PDE. Factorization solution rational exponential parts enables us construct analytic with...

a modified f-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (nlpdes) is discussed. we use this method to construct many new solutions to the nonlinear whitham-broer-kaup system (1+1)-dimensional. the solutions obtained include jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

A modified F-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

A finite-difference scheme arising from fourth order rational approximants to the matrix-exponential term in a two-time level recurrence relation has been proposed for the numerical solution of the modified Burgers' equation already known in the bibliography. The method leads to the solution of a nonlinear system. To overcome this difficulty a linearized scheme is proposed.

In this paper, we study asymptotic properties of rational functions that interpolate the exponential function. The interpolation is performed with respect to a triangular scheme of complex conjugate points lying in bounded rectangular domains included in the horizontal strip |Im z|<2?. Moreover, the height of these domains cannot exceed some upper bound which depends on the type of rational fun...