We use a variational method based on the principle of least action to obtain approximate time-dependent single soliton solutions to the KdV equation. A class of trial variational functions of the form u(x, t) = −A(t) exp [ −β(t) |x− q(t)| ] , with n a continuous real variable, is used to parametrize timedependent solutions. We find that this class of trial functions leads to soliton-like soluti...

In this paper, we derive a Bäcklund transformation for the supersymmetric Kortwegde Vries equation. We also construct a nonlinear superposition formula, which allows us to rebuild systematically for the supersymmetric KdV equation the soliton solutions of Carstea, Ramani and Grammaticos. The celebrated Kortweg-de Vries (KdV) equation was extended into super framework by Kupershmidt [3] in 1984....

The objective of this paper is to use the Pfaffian technique to construct different classes of exact Pfaffian solutions and N -soliton solutions to some of the generalized integrable nonlinear partial differential equations in (3+1) dimensions. In this paper, I will show that the Pfaffian solutions to the nonlinear PDEs are nothing but Pfaffian identities. Solitons are among the most beneficial...

The different dynamical features underlying soliton interactions in coupled nonlinear Schrödinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by explicitly constructing multisoliton solutions (up to four-soliton solutions) for two-coupled and arbitrary N-coupled nonlinear Schrödinger equations using the Hiro...

Solitons are an important class of solutions to nonlinear differential equations which appear in different areas physics and applied mathematics. In this study we provide a general overview the Hirota method is one most powerful tool finding multi-soliton wave evaluation equations. Bright dark soliton Schrödinger equation discussed detail

We derive the soliton matrices corresponding to an arbitrary number of higherorder normal zeros for the matrix Riemann–Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial differential equations integrable through the matrix R...