Dimensional Kadomtsev Research Articles

Lie group analysis and conserved vectors of a generalized (3+1)-dimensional Kadomtsev- Petviashvili Benjamin-Bona-Mahony equation with power law nonlinearity

In this paper, our aim is to compute exact solutions for the generalized (3+1)-dimensional KadomtsevPetviashvili Benjamin-Bona–Mahony (gnKP-BBM) equation by invoking an effective method, namely the Lie symmetry technique. Firstly, we derive the infinitesimals and write down the Lie symmetries. Using these symmetries the gnKP-BBM equation is reduced to various nonlinear ordinary differential equations (NLODEs). Thereafter, solutions of the NLODEs are derived by using the Jacobi elliptic cosine method, the (G 0 /G)-expansion method, the simplest equation technique and Kudryashov’s method. Conclusively, we derive conservation laws of the gnKP-BBM equation by using the Ibragimov’s method.

Exact solutions and conservation laws of a new fourth-order nonlinear (3+1)-dimensional Kadomtsev- Petviashvili-like equation

Exact solutions and conservation laws of a new fourth-order nonlinear (3+1)-dimensional Kadomtsev- Petviashvili-like equation

Lax integrability and soliton solutions of the (2 + 1)- dimensional Kadomtsev– Petviashvili– Sawada–Kotera– Ramani equation

In this paper, a new (2 + 1)-dimensional nonlinear evolution equation is investigated. This equation is called the Kadomtsev–Petviashvili–Sawada–Kotera–Ramani equation, which can be seen as the two-dimensional extension of the Korteweg–de Vries–Sawada–Kotera–Ramani equation. By means of Hirota’s bilinear operator and the binary Bell polynomials, the bilinear form and the bilinear Bäcklund transformation are obtained. Furthermore, by application of the Hopf-Cole transformation, the Lax pair is also derived. By introducing the new potential function, infinitely many conservation laws are constructed. Therefore, the Lax integrability of the equation is revealed for the first time. Finally, as the analytical solutions, the N-soliton solutions are presented.

Dynamics of abundant solutions to the generalized (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

The present paper is devoted to discussion of (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili (gBKP) equation from point of view of their multi-soliton solutions and localized solutions associated with multi-soliton solutions. Firstly, taking advantage of the Bell-polynomial approach, we construct the Hirota bilinear form of (1.1). Based on that, the multi-soliton solutions are also singled out. Subsequently, the (3+1)-dimensional gBKP equation is also found to allow fruitful localized solutions, including breather, lump, rogue wave, and hybrid solutions. These results obtained in this work adequately illustrate the effectiveness of the long wave limit method and complex conjugate technique, which are expected to be employed to obtain more abundant exact solutions.

Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas

In this paper, the fractional order models are used to study the propagation of ion-acoustic waves in ultrarelativistic plasmas in nonplanar geometry (cylindrical). Firstly, according to the control equations, (2 + 1)-dimensional (2D) cylindrical Kadomtsev–Petviashvili (CKP) equation and 2D cylindrical-modified Kadomtsev–Petviashvili (CMKP) equation are derived by using multiscale analysis and reduced perturbation methods. Secondly, using the semi-inverse method and the fractional variation principle, the abovementioned equations are derived the time-space fractional equations (TSF-CKP and TSF-CMKP). Furthermore, based on the fractional order transformation, the 1-decay mode solution of the TSF-CKP equation is obtained by using the simplified homogeneous balance method, and using the generalized hyperbolic-function method, the exact analytic solution of TSF-CMKP equation is obtained. Finally, the effects of the phase speedλ, electron number density (throughβ3) and the fractional orderα,β,ωon the propagation of ion-acoustic waves in ultrarelativistic plasmas are analyzed.

Lie group analysis and invariant solutions of (3+1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation

We study the (3[Formula: see text]+[Formula: see text]1)-dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation by using the Lie group analysis method. The reduction equations are given out by selecting different constants and new explicit solutions are also presented by the Riccati equation expansion and the power series expansion.

New dual-mode Kadomtsev\u2013Petviashvili model with strong\u2013weak surface tension: analysis and application

Dual-mode (2+1)-dimensional Kadomtsev–Petviashvili (DMKP) equation is a new model which represents the spread of two simultaneously directional waves due to the involved term “u_{tt}(x,y,t)” in its equation. We present the construction of DMKP and search for possible solutions. The innovative tanh-expansion method and Kudryashov technique will be utilized to find the necessary constraint conditions which guarantee the existence of soliton solutions to DMKP. Supportive 3D plots will be provided to validate our findings.

Rogue waves and lump solitons for a -dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics

Under investigation is a -dimensional B-type Kadomtsev–Petviashvili equation, which has applications in the propagation of non-linear waves in fluid dynamics. Through the Hirota method and the extended homoclinic test technique, we obtain the breather-type kink soliton solutions and breather rational soliton solutions. Rogue wave solutions are derived, which come from the derivation of breather rational solitons with respect to x. Amplitudes of the breather-type kink solitons and rogue waves decrease with a non-zero parameter in the equation, , increasing when . In addition, dark rogue waves are derived when . Furthermore, with the aid of the Hirota method and symbolic computation, two types of the lump solitons are obtained with the different choices of the parameters. We graphically study the lump solitons related to the parameter , and amplitude of the lump soliton is negatively correlated with when .

A modified form of $${\left(\frac{G^\prime}{G}\right)}$$ G ′ G -expansion method and its application to Potential Kadomtsev–Petviashvili (PKP) equation

In this paper, we present a modified form of the \({(\frac{G^\prime}{G})}\) -expansion method and as a application proposed to construct exact solutions of (2 + 1)-dimensional Potential Kadomtsev–Petviashvili equation. Each of the obtained solutions, namely hyperbolic function solutions, trigonometric function solutions and rational solutions contains an explicit linear function of the variables in the considered equation. It is shown that the proposed method with the help of symbolic computation provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

LAX PAIR, BINARY DARBOUX TRANSFORMATION AND NEW GRAMMIAN SOLUTIONS OF NONISOSPECTRAL KADOMTSEV–PETVIASHVILI EQUATION WITH THE TWO-SINGULAR-MANIFOLD METHOD

In this letter, the two-singular-manifold method is applied to the (2+1)-dimensional nonisospectral Kadomtsev–Petviashvili equation with two Painlevé expansion branches to determine auto-Bäcklund transformation, Lax pairs and Darboux transformation. Based on the two obtained Lax pairs, the binary Darboux transformation is constructed and then the Nth iterated transformation formula in the form of Grammian is also presented. By using these Darboux transformations, we obtain some new grammian solutions.