We construct a new multi-component CKP hierarchy based on the eigenfunction symmetry reduction. It contains two types of CKP equation with self-consistent sources which Lax representations are presented. Also it admits reductions to k−constrained CKP hierarchy and to a (1+1)-dimensional soliton hierarchy with self-consistent source, which include two types of Kaup-Kuperschmidt equation with sel...

A systematic investigation of certain higher order or deformed soliton equations with (1 + 1) dimensions, from the point complete integrability, is presented. Following procedure Ablowitz, Kaup, Newell and Segur (AKNS) we find that version Nonlinear Schrodinger equation, Hirota equation AKNS admit Lax pairs. We report each identified possesses Painleve property for partial differential admits t...

In this paper, the space–time fractional Whitham–Broer–Kaup equations are investigated. By means of new scaling transformations, nonlinear system different time and space orders is transformed to integer one. The multiple solitary solutions periodic obtained, respectively. All those given exactly by introducing which makes our study unique from most existing studies. It expected that exact for ...

In this paper, the Lakshmanan-Porsezian-Daniel (LPD) equation is considered. This integrable and admits Lax pair. The LPD generalization of nonlinear Schrodinger (NLS) described by Ablowitz-Kaup-Newell-Segur (AKNS) system. Using sine-cosine method hyperbolic tangent a variety new exact solutions are obtained. These methods effective tools for searching partial differential equations in mathemat...

In this paper, the Exp -function method with the aid of symbolic computational system is used to obtain the exact travelling wave and solitary solutions of the Fitzhugh-Nagumo (FN), Modified Liouville equations and bi-directional Kaup-Kupershmidt (bKK) equation (sixth-order nonlinear equation). An attempt has been made to show the capabilities and wide-range applications of the Exp -function me...

In this paper, the Painlevé integrable property of (1 + 1)-dimensional generalized Broer–Kaup (gBK) equations is first proven. Then, Bäcklund transformations for gBK are derived by using truncation. Based on a special case transformations, linearized into heat conduction equation. Inspired reduced Burgers Starting from linear equation, two forms N-soliton solutions and rational with singularity...

This paper presents the semi-analytical analysis of fractional-order non-linear coupled system Whitham-Broer-Kaup equations. An iterative process is designed to analyze analytical findings specified partial fractional derivatives scheme utilizing Yang transformation with Adomian technique. The derivative considered in sense Caputo-Fabrizio. Two numerical problems show suggested method. Moreover...

We construct the classical Poisson structure and r-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds of classical, dynamical Yang-Baxter structures. To illustrate the method we present the r-matrices associated with the constrained flows of the Kaup-Newell, KdV...

A construction of the bi-Hamiltonian structures for integrable systems on regular time scales is presented. The trace functional on an algebra of δ-pseudo-differential operators, valid on an arbitrary regular time scale, is introduced. The linear Poisson tensors and the related Hamiltonians are derived. The quadratic Poisson tensors is given by the use of the recursion operators of the Lax hier...