Dimensional Generalized Broer Kaup System Research Articles

Solitary wave fission and fusion in the (2+1)-dimensional generalized Broer–Kaup system

Via a special Painlevé–Bäcklund transformation and the linear superposition theorem, we derive the general variable separation solution of the (2 + 1)-dimensional generalized Broer–Kaup system. Based on the general variable separation solution and choosing some suitable variable separated functions, new types of V-shaped and A-shaped solitary wave fusion and Y-shaped solitary wave fission phenomena are reported.

Non-Lie symmetry groups and new exact solutions of a (2+1)-dimensional generalized Broer–Kaup system

By the modified CK’s direct method, the symmetry groups theorem of a (2+1)-dimensional generalized Broer–Kaup system is derived. Based upon the results, Lie point symmetry groups and new exact solutions of a (2+1)-dimensional generalized Broer–Kaup system are obtained.

Construction of new exact rational form non-travelling wave solutions to the (2 + 1)-dimensional generalized Broer–Kaup system

With the aid of symbolic computation Maple, several new families of rational form variable separation solutions with three arbitrary functions to the (2 + 1)-dimensional generalized Broer–Kaup system are derived by using an improved mapping approach and a variable separation approach. These solutions include rational solitary wave solutions, periodic wave solutions and rational wave solutions. The properties of the novel localized excitation are revealed by some figures.

New exact solutions for the (2 + 1)-dimensional generalized Broer–Kaup system

The (1 + 1)-dimensional Broer–Kaup system, which describes the propagation of shallow water waves, is extended to a generalized (2 + 1)-dimensional model with Painleve property. In this paper, based on the general variable separation approach and two extended Riccati equations, we first find several new families of exact soliton-like solutions and periodic-like wave solutions with arbitrary functions for the (2 + 1)-dimensional simplified generalized Broer–Kaup (GBK) system ( B = 0). Abundant new localized excitations can be found by selecting appropriate functions. After that, we consider the conditions of ( B ≠ 0) to the GBK, and several new results are obtained.

Complex Wave Excitations in GeneralizedBroer–Kaup System

Starting from an improved projective method and a linear variableseparation approach, new families of variable separation solutions(including solitary wave solutions, periodic wave solutions andrational function solutions) with arbitrary functions for the(2+1)-dimensional generalized Broer–Kaup (GBK) system are derived.Usually, in terms of solitary wave solutions and/or rationalfunction solutions, one can find abundant important localizedexcitations. However, based on the derived periodic wave solutionin this paper, we reveal some complex wave excitations in the(2+1)-dimensional GBK system, which describe solitons moving on aperiodic wave background. Some interestingevolutional properties for these solitary waves propagating onthe periodic wave background are also briefly discussed.

Symmetry and Similarity Solutions of a (2+1)-DimensionalGeneralized Broer–Kaup System

We study the symmetries of a (2+1)-dimensional generalizedBroer–Kaup system by means of the classical Lie group theory.The corresponding group algebra is constructed. Based on thesymmetries, several types of similarity solutions are obtained.

Nonlinear excitations and “peakons” of a (2+1)-dimensional generalized Broer-Kaup system

Shallow water waves and a host of long wave phenomena are commonly investigated by various models of nonlinear evolution equations. Examples include the Korteweg–de Vries, the Camassa–Holm, and the Whitham–Broer–Kaup (WBK) equations. Here a generalized WBK system is studied via the multi-linear variable separation approach. A special class of wave profiles with discontinuous derivatives (“peakons”) is developed. Peakons of various features, e.g. periodic, pulsating or fractal, are investigated and interactions of such entities are studied.

New Types of Solitons with Fusion and Fission Properties in the (2+1)-Dimensional Generalized Broer-Kaup System

In this paper, by virtue of a special Painlevé-Bäcklund transformation and the linear superposition theorem, the general variable separation solution with an arbitrary number of variable separated functions of the generalized Broer-Kaup (GBK) system is obtained. Based on the general variable separation solution with some suitable variable separated functions, new types of the V-shaped soliton fusion and Y-shaped soliton fission are firstly investigated. - PACS numbers: 05.45.Yv, 02.30.Jr, 02.03Ik

Infinite generation of soliton-like solutions for the (2+1) -dimensional generalized Broer–Kaup system

There is a long-standing interest in obtaining exact analytical solutions of nonlinear evolution equations since the exact solutions often model natural phenomena and facilitate the testing of numerical solvers as well as aiding in the stability analysis. In this paper, using a Burgers equation-based constructive method, we obtain a formula which can be applied to generate infinite sequences of exact solutions for the (2+1)-dimensional generalized Broer–Kaup (GBK) system. According to some explicit exact solutions, we also graphically reveal some interesting soliton-like wave motions which may be observable in the future experiments.

Evolutional Properties of Localized Excitationsfor Generalized Broer–Kaup Systemin (2+1) Dimensions

Using a special Painlevé–Bäcklund transformation as wellas the extended mapping approach and the linear superpositiontheorem, we obtain new families of variable separation solutionsto the (2+1)-dimensional generalized Broer–Kaup (GBK) system. Basedon the derived exact solution, we reveal some novel evolutionalbehaviors of localized excitations, i.e. fission and fusion phenomenain the (2+1)-dimensional GBK system.

Quasi-periodic and non-periodic waves in the (2+1)-dimensional generalized Broer–Kaup system

Abstract For a higher-dimensional integrable nonlinear dynamical system, there are abundant coherent soliton excitations. With the aid of an improved projective Riccati equation approach, the paper obtains several types of exact solutions to the (2 + 1)-dimensional generalized Broer–Kaup system, including multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. From which, new quasi-periodic and non-periodic excitations for the system are studied by means of the Jacobi elliptic functions with the space–time-dependent modulus.

Some Coherent Excitations for the (2+1)-Dimensional Generalized Broer-Kaup System

Using a projective Riccati equation, several types of solutions of the (2+1)-dimensional generalized Broer-Kaup system are obtained, including multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. From these, two sets of wave packets are expressed as rational functions of elliptic functions. Especially, peculiar wave patterns that are localized in one direction but periodic in the other direction arise by taking the long wave length limit in one spatial variable. Also exponentially localized wave patterns, which differ from the known dromions, are obtained by taking the long wave length limit in both spatial variables. The interactions of two dromions with inelastic and elastic behaviors are presented

A New Class of (2+1)-Dimensional Combined Structures with Completely Elastic and Non-Elastic Interactive Properties

Taking the new (2+1)-dimensional generalized Broer-Kaup system as an example, we obtain an exact variable separation excitation which can describe some quite universal (2+1)-dimensional physical models, with the help of the extended homogeneous balance method. Based on the derived excitation, a new class of combined structures, i. e., semifolded solitary waves and semifoldons, is defined and studied. The interactions of the semifolded localized structures are illustrated both analytically and graphically. - PACS numbers: 05.45.Yv, 02.30.Jr, 02.30.Ik

Fission, fusion and annihilation in the interaction of localized structures for the (2+1)-dimensional generalized Broer–Kaup system

Abstract Based on the WTC truncation method and the general variable separation approach (GVSA), we have first found a general solution including three arbitrary functions for the (2 + 1)-dimensional simplified generalized Broer–Kaup (GBK) system (B = 0). A class of double periodic wave solutions is obtained by selecting these arbitrary functions appropriately. The interaction properties of the periodic waves are numerically studied and found to be non-elastic. Limit cases are considered and some new localized coherent structures are obtained, the interaction properties of these solutions reveal that some of them are completely elastic and some are non-completely elastic. After that, starting from the (2 + 1)-dimensional GBK system (B ≠ 0) and using the variable separation approach (VSA) including two arbitrary functions in the general solution, we have constructed by selecting the two arbitrary functions appropriately a rich variety of new coherent structures. The interaction properties of these structures reveal new physical properties like fusion, fission, or both and present mutual annihilation of these solutions as time increasing. The annihilation in this model has found to be rule by the parameter K1, when this parameter is taken to be zero, the annihilation disappears in this model and the above mentioned structures recover the solitonic structure properties.

New exact solutions and fractal patterns of generalized Broer–Kaup system via a mapping approach

Abstract With the help of an extended mapping approach, a new type of variable separation solution with two arbitrary functions of the (2 + 1)-dimensional generalized Broer–Kaup (GBK) system is derived. Based on the derived solitary wave excitation, we reveal some regular fractal and stochastic fractal patterns in the (2 + 1)-dimensional GBK system.

Variable Separation Solutions of Generalized Broer–Kaup Systemvia a Projective Method

Using an extended projective method, a new type of variableseparation solution with two arbitrary functions of the(2+1)-dimensional generalized Broer-Kaup system (GBK) is derived.Based on the derived variable separation solution, some speciallocalized coherent soliton excitations with or without elasticbehaviors such as dromions, peakons, and foldons etc. arerevealed by selecting appropriate functions in this paper.

New Explicit Exact Solutions to (2+1)-Dimensional GeneralizedBroer–Kaup System

A nonlinear transformation and somemulti-solition solutions for the (2+1)-dimensional generalizedBroer–Kaup (GBK) system is first given by using the homogeneousbalance method. Then starting from the nonlinear transformation,we reduce the (2+1)-dimensional GBK system to a simple linearevolution equation. Solving this equation, we can obtain some newexplicit exact solutions of the original equationsby means of the extended hyperbola function method.