The inverse scattering transform allows explicit construction of solutions to many physically significant nonlinear wave equations. Notably, this method can be extended fractional evolution equations characterized by anomalous dispersion using completeness suitable eigenfunctions the associated linear problem. In diffusion, mean squared displacement is proportional $t^{\alpha}$, $\alpha>0$, whi...

The “particle-in-a-box” problem is investigated for a relativistic particle obeying the Klein–Gordon equation. To find bound states, standard methods known from elementary non-relativistic quantum mechanics can only be employed “shallow” wells. For deeper wells, when confining potentials become supercritical, we show that method based on scattering expansion accounts Klein tunneling (undamped p...

In this study, the generalized coupled nonlinear Schrödinger–KdV (NLS–KdV) system is investigated to obtain new optical soliton solutions. This appears as a model for reciprocity between long and short waves in various physical settings. Different kinds of solutions including dark, bright, combined dark-bright, singular are obtained using two effective methods namely, extended sinh–Gordon equat...

in this paper a modification of he's variational iteration method (vim) has been employed to solve dung and riccati equations. sometimes, it is not easy or even impossible, to obtain the first few iterations of vim, therefore, we suggest to approximate the integrand by using suitable expansions such as taylor or chebyshev expansions.

Abstract In this work, we investigate the solutions of (2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili (BKP) equation by three powerful analytical methods: $$\exp _{a}$$ exp a function method, $$(\frac{G'}{G})$$ ( <mml:msu...

In this work, we use two different analytic schemes which are the Sine-Gordon expansion technique and modified exp -expansion function to construct novel exact solutions of non-linear Schrödinger equation, describing gravity waves in infinite deep water, sense conformable derivative. After getting various travelling wave solutions, plot 3D, 2D contour surfaces present behaviours obtained soluti...

With the aid of symbolic computation, the sinh-Gordon equation expansion method is extended to seek Jacobi elliptic function solutions of (2+1)-dimensional long wave-short wave resonance interaction equation, which describe the long and short waves propagation at an angle to each other in a two-layer fluid. As a result, new Jacobi elliptic function solutions are obtained. When the modulus m of ...

Abstract We derive a modulation theory for the resolution of radially symmetric kink waves governed by multi-dimensional sine-Gordon equation. Whitham is developed to explain return an expanding wave, as well predicting its maximum expansion radius and time. Comparisons with full numerical solutions equation show that gives excellent predictions not only returning time radius, but also details ...

We study the mechanism of particle creation in context emergent universe (EU) scenario which is privileged by certain important characteristics such as absence time-like singularity. EU asymptotically coincides with an Einstein static model infinite past and it approaches to a de Sitter expansion phase at late times. By introducing conformal time, we obtain solution Klein-Gordon equation applyi...

We derive approximate expressions for the dispersion relation of the nonlinear Klein-Gordon equation in the case of strong nonlinearities using a method based on the linear delta expansion. All the results obtained in this article are fully analytical, never involve the use of special functions, and can be used to obtain systematic approximations to the exact results to any desired degree of ac...