Closed-form solutions and conservation laws of a generalized Hirota–Satsuma coupled KdV system of fluid mechanics

KdV and Almost Conservation Laws

In this article we illustrate a new method to extend local wellposedness results for dispersive equations to global ones. The main ingredient of this method is the definition of a family of what we call almost conservation laws. In particular we analyze the Korteweg-de Vries initial value problem and we illustrate in general terms how the “algorithm” that we use to formally generate almost cons...

Water Wave Solutions of the Coupled System Zakharov-Kuznetsov and Generalized Coupled KdV Equations

An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solution...

Exact solutions and conservation laws of a coupled integrable dispersionless system

In this paper we study the coupled integrable dispersionless system (CIDS), which arises in the analysis of several problems in applied mathematics and physics. Lie symmetry analysis is performed on CIDS and symmetry reductions and exact solutions with the aid of simplest equation method are obtained. In addition, the conservation laws of the CIDS are also derived using the multiplier (and homo...

Generalized Beltrami Flows and Other Closed-form Solutions of an Unsteady Viscoelastic Fluid

Nonlocal conservation laws for supersymmetric KdV equations

The nonlocal conservation laws for the N=1 supersymmetric KdV equation are shown to be related in a simple way to powers of the fourth root of its Lax operator. This provides a direct link between the supersymmetry invariance and the existence of nonlocal conservation laws. It is also shown that nonlocal conservation laws exist for the two integrable N=2 supersymmetric KdV equations whose recur...