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Two effective approaches for solving fractional generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves

Journal of Ocean Engineering and Science, 2019
In this article, two different methods, namely sub-equation method and residual power series method, have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations, which is a coupled KdV model.
Ali Kurt +6 more
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GROUP FOLIATION OF DIFFERENTIAL EQUATIONS USING MOVING FRAMES

Forum of Mathematics, Sigma, 2015
We incorporate the new theory of equivariant moving frames for Lie pseudogroups into Vessiot’s method of group foliation of differential equations. The automorphic system is replaced by a set of reconstruction equations on the pseudogroup jets.
ROBERT THOMPSON, FRANCIS VALIQUETTE
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Construction of an infinite-dimensional family of exact solutions of the Klein–Gordon equation by the hypercomplex method

Partial Differential Equations in Applied Mathematics
The Klein–Gordon equation is one of the fundamental equations of mathematical physics. Therefore, it is important to have exact solutions to this equation. There are many methods for constructing exact solutions to the Klein–Gordon equation.
Vitalii Shpakivskyi
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Perturbational blowup solutions to the compressible Euler equations with damping. [PDF]