In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examp...

Applying braided Yang–Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and q-anyonic models as well as nonlinear Schrödinger equation (NLS) and the derivative NLS quantum field models involving anyonic operators, N -particle sectors of which yield the well known anyon gases...

This paper investigates the existence of solutions of the nonlinear fractional differential equation { Du(t) + f(t, u(t),Du(t)) = 0, 0 < t < 1, 3 < α ≤ 4, u(0) = u′(0) = u′′(0) = 0, u(1) = u(ξ), 0 < ξ < 1, where D is the Caputo fractional derivative, β > 0, α− β ≥ 1. The peculiarity of this equation is that the nonlinear term depends on the fractional derivative of the unknown function, compare...

We make use of fractional derivative, recently proposed by Caputo and Fabrizio, to modify the nonlinear Nagumo diffusion and convection equation. The proposed fractional derivative has no singular kernel considered as a filter. We examine the existence of the exact solution of the modified equation using the method of fixed-point theorem. We prove the uniqueness of the exact solution and presen...

The fractional derivatives in the sense of Caputo, and the homotopy analysis method (HAM) are used to construct the approximate solutions for nonlinear fractional dispersive long wave equation with reaspect to time fractional derivative. The HAM contains a certain auxiliary parameter which provides us with a simple way to adjust and control the convergence region and rate of convergence of the ...

The nonlinear Schrödinger (NLS) equation is a fundamental model for the nonlinear propagation of light pulses in optical fibers. We consider an integrable generalization of the NLS equation which was first derived by means of bi-Hamiltonian methods in [A. S. Fokas, Phys. D 87 (1995), 145–150]. The purpose of the present paper is threefold: (a) We show how this generalized NLS equation arises as...

in this work, we have applied elzaki transform and he&apos;s homotopy perturbation method to solvepartial dierential equation (pdes) with time-fractional derivative. with help he&apos;s homotopy per-turbation, we can handle the nonlinear terms. further, we have applied this suggested he&apos;s homotopyperturbation method in order to reformulate initial value problem. some illustrative examples...

This paper presents the formulation of time-fractional Klein-Gordon equation using the Euler-Lagrange variational technique in the Riesz derivative sense and derives an approximate solitary wave solution. Our results witness that He’s variational iteration method was very efficient and powerful technique in finding the solution of the proposed equation. The basic idea described in this paper is...