New Travelling Wave Solutions of Two Nonlinear Physical Models by Using a Modified Tanh-Coth Method

In this work, a modified tanh – coth method is used to derive travelling wave solutions for (2 + 1)-dimensional Zakharov-Kuznetsov (ZK) equation and (3 + 1)-dimensional Burgers equation. A new variable is used to solve these equations and established new travelling wave solutions. </jats:p

On the solutions of the (1+1) and (2+1)-dimensional higher-order Broer-Kaup systems

In this work we study the (1+1) and (2+1)-dimensional higher-order Broer-Kaup (HBK) systems. The HBK systems were obtained from the inner parameter dependent symmetry constraints of the Kadomtsev-Petviashvili (KP) equation. The Bäcklund transformations are used for a reliable treatment of these systems. We obtain multiple soliton solutions for the underlying systems. Moreover, we use a variety of hyperbolic functions methods and trigonometric methods to determine a variety of travelling wave solutions and periodic solutions

A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems

AbstractIn this paper, we propose an algorithm for solving the nonlinear two-point boundary value problem that has at least one positive solution [1–6] for λ in a compatible interval. Our method stems mainly from combining the decomposition series solution obtained by Adomian decomposition method with Padé approximates. The validity of the approach is verified through illustrative numerical example