Caudrey-Dodd-Gibbon-Sawada-Kotera Research Articles

Different-Periodic Travelling Wave Solutions for Nonlinear Equations**The project supported by the National Outstanding Youth Foundation of China under Grant No. 19925522, National Natural Science Foundation of China under Grant No. 90203001, and the Natural Science Foundation of ZheJiang Province of China under Grant No. 102053

Using Jacobi elliptic function linear superposition approach for the (1+1)-dimensional Caudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation and the (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equation, many new periodic travelling wave solutions with different periods and velocities are obtained based on the known periodic solutions. This procedure is crucially dependent on a sequence of cyclic identities involving Jacobi elliptic functions sn(), cn(), and dn().

New Exact Solutions of the CDGSK Equation Related to a Non-local Symmetry

A non-local symmetry of the Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation has been used for finding exact solution in two different ways. Firstly, using the standard prolongation approach, we obtain the finite Lie Bäcklund transformation and the single soliton solution. Secondly, combining some local symmetries and the nonlocal symmetry, we get the group invariant solution which is described by the Weierstrass elliptic function and is deduced to the so-called interacting soliton for a special parameter.

Twelve sets of symmetries of the Caudrey-Dodd-Gibbon-Sawada-Kotera equation

Using the pseudopotential of the Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation, the inverse recursion operator of CDGSK is exhibited explicitly. Twelve sets of the CDGSK equation are obtained by acting the recursion operator and its inverse on the trivial symmetry and a time dependent symmetry. Only one set of them is time dependent.

The reverse bending fatigue strength of drill pipes under the effect of drilling fluids: Helbig, R. and Vogt, G.H. Mannesmann Forschungsber. 1988 (1059), 510–514 (in German)

In this work, the analytic solutions for different types of nonlinear partial differential equations are obtained using the multiple Exp-function method. We consider the stated method for the (3+1)-dimensional generalized shallow water-like (SWL) equation, the (3+1)-dimensional Boiti–Leon- Manna–Pempinelli (BLMP) equation, (3+1)-dimensional generalized variable-coefficient B-type Kadomtsev–Petviashvili (VC B-type KP) equation and the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada (CDGKS) equation. We obtain multi classes of solutions containing one-soliton, two-soliton, and triple-soliton solutions. All the computations have been performed using the software package Maple. The obtained solutions include three classes of soliton wave solutions in terms of one-wave, two-waves, and three-waves solutions. Then the multiple soliton solutions are presented with more arbitrary autocephalous parameters, in which the one, two, and triple solutions localized in all directions in space. Moreover, the obtained solutions and the exact solutions are shown graphically, highlighting the effects of non-linearity. The different types of obtained solutions of aforementioned nonlinear equations arising in fluid dynamics and nonlinear phenomena.