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1.
Under investigation in this paper are two coupled integrable dispersionless (CID) equations modeling the dynamics of the current-fed string within an external magnetic field. Through a set of the dependent variable transformations, the bilinear forms for the CID equations are derived. Based on the Hirota method and symbolic computation, the analytic N-soliton solutions are presented. Infinitely many conservation laws for the CID equations are given through the known spectral problem. Propagation characteristics and interaction behaviors of the solitons are analyzed graphically. 相似文献
2.
Bilinearization and soliton solutions of N=1 supersymmetric coupled dispersionless integrable system
Arifa Mirza 《Journal of Nonlinear Mathematical Physics》2017,24(1):107-115
An N=1 supersymmetric generalization of coupled dispersionless (SUSY-CD) integrable system has been proposed by writing its superfield Lax representation. It has been shown that under a suitable variable transformation, the SUSY-CD integrable system is equivalent to N=1 supersymmetric sine-Gordon equation. A superfield bilinear form of SUSY-CD integrable system has been proposed by using super Hirota operator. Explicit expressions of superfield soliton solutions of SUSY-CD integrable system have been obtained by using the Hirota method. 相似文献
3.
YU Fa-Jun LI Li 《理论物理通讯》2009,51(1):23-26
It is shown that the Kronecker product can be applied to construct a new integrable coupling system of soliton equation hierarchy in this paper. A direct application to the Burgers spectral problem leads to a novel soliton equation hierarchy of integrable coupling system. It indicates that the Kronecker product is an efficient and straightforward method to construct the integrable couplings. 相似文献
4.
In this paper, two types of the (2+1)-dimensional breaking soliton equations axe investigated, which describe the interactions of the Riemann waves with the long waves. With symbolic computation, the Hirota bilineax forms and Bgcklund transformations are derived for those two systems. Furthermore, multisoliton solutions in terms of the Wronskian determinant are constructed, which are verified through the direct substitution of the solutions into the bilineax equations. Via the Wronskian technique, it is proved that the Bgcklund transformations obtained are the ones between the ( N - 1)- and N-soliton solutions. Propagations and interactions of the kink-/bell-shaped solitons are presented. It is shown that the Riemann waves possess the solitonie properties, and maintain the amplitudes and velocities in the collisions only with some phase shifts. 相似文献
5.
Investigated in this paper is the generalized nonlinear Schrodinger equation with radial symmetry. With the help of symbolic computation, the one-, two-, and N-soliton solutions are obtained through the bilinear method. B~cklund transformation in the bilinear form is presented, through which a new solution is constructed. Graphically, we have found that the solitons are symmetric about x = O, while the soliton pulse width and amplitude will change along with the distance and time during the propagation. 相似文献
6.
We study the integrable discretization of the coupled integrable dispersionless equations. Two semi-discrete version and one full-discrete version of the system are given via Hirota's bilinear method. Soliton solutions for the derived discrete systems are also presented. 相似文献
7.
The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions (including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions) for the new (2+1)-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field. 相似文献
8.
We propose a method to construct the integrable Rosochatius deformations for an integrable couplings equations hierarchy. As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy with self-consistent sources and its Lax representation are presented. 相似文献
9.
In this paper, by introducing a new transformation, the bilinear
form of the coupled integrable dispersionless (CID) equations is
derived. It will be shown that this bilinear form is easier to
perform the standard Hirota process. One-, two-, and three-soliton
solutions are presented. Furthermore, the N-soliton solutions are
derived. 相似文献
10.
This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more generalvariable separation solutions with two arbitrary functions of (1+1)-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p(x) and q(t) inour solutions, the annihilation phenomena of the flat-basin soliton, arch-basin soliton, and flat-top soliton are discussed. 相似文献
11.
YANG Jian-Rong MAO Jie-Jian 《理论物理通讯》2008,50(10):809-813
A special coupled KdV equation is proved to be the Painleve property by the Kruskal's simplification of WTC method. In order to search new exact solutions of the coupled KdV equation, Hirota's bilinear direct method and the conjugate complex number method of exponential functions are applied to this system. As a result, new analytical eomplexiton and soliton solutions are obtained synchronously in a physical field. Then their structures, time evolution and interaction properties are further discussed graphically. 相似文献
12.
<正>A new coupled integrable dispersionless equation is presented by considering a spectral problem.A Darboux transformation for the resulting coupled integrable dispersionless equation is constructed with the help of spectral problems.As an application,the N-soliton solution of the coupled integrable dispersionless equation is explicitly given. 相似文献
13.
The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq–Burgers equation
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This paper studies the coupled Burgers equation and the high-order Boussinesq–Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink (soliton) solutions and multiple-singular-kink (soliton) solutions are derived for the two equations. 相似文献
14.
Soliton solution and interaction property for a coupled modified Korteweg-de Vries (mKdV) system
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Hirota's bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries (mKdV) system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this (1+1)-dimensional integrable coupled model. 相似文献
15.
In the wake of the recent investigation of new coupled integrable dispersionless equations by means of the Darboux transformation [Zhaqilao,et al.,Chin.Phys.B 18(2009) 1780],we carry out the initial value analysis of the previous system using the fourth-order Runge-Kutta's computational scheme.As a result,while depicting its phase portraits accordingly,we show that the above dispersionless system actually supports two kinds of solutions amongst which the localized traveling wave-guide channels.In addition,paying particular interests to such localized structures,we construct the bilinear transformation of the current system from which scattering amongst the above waves can be deeply studied. 相似文献
16.
ZHU Hong-Wu TIAN Bo MENG Xiang-Hua LI Juan XU Tao 《理论物理通讯》2008,50(9):689-695
A bilinear Baecklund transformation is presented for the three coupled higher-order nonlinear Schroedinger equations with the inclusion of the group velocity dispersion, third-order dispersion and Kerr-law nonlinearity, which can describe the dynamics of alpha helical proteins in living systems as well as the propagation of ultrashort pulses in wavelength-division multiplexed system. Starting from the Baecklund transformation, the analytical soliton solution is obtained from a trivial solution. Simultaneously, the N-soliton-like solution in double Wronskian form is constructed, and the corresponding proof is also given via the Wronskian technique. The results obtained from this paper might be valuable in studying the transfer of energy in biophysics and the transmission of light pulses in optical communication systems. 相似文献
17.
According to the conjecture based on some known facts of integrable
models, a new (2+1)-dimensional supersymmetric integrable bilinear
system is proposed. The model is not only the extension of the known
(2+1)-dimensional negative Kadomtsev--Petviashvili equation but also
the extension of the known (1+1)-dimensional supersymmetric
Boussinesq equation. The infinite dimensional Kac--Moody--Virasoro
symmetries and the related symmetry reductions of the model are
obtained. Furthermore, the traveling wave solutions including
soliton solutions are explicitly presented. 相似文献
18.
We investigate a kind of solitons in the two-component Bose-Einstein condensates with axisymmetric configurations in the R2 × S1 space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional (3D) skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross-Pitaevskii equations in imaginary time. 相似文献
19.
Under investigation in this paper are two coupled integrable dispersionless (CID) equations modeling the dynamics of the current-fed string within an external magnetic field. Through a set of the dependent variable transformations, the bilinear forms for the CID equations are derived. Based on the Hirota method and symbolic computation, the analytic N-soliton solutions are presented. Infinitely many conservation laws for the CID equations are given through the known spectral problem. Propagationcharacteristics and interaction behaviors of the solitons are analyzed graphically. 相似文献
20.
The prolongation structure methodologies of Wahlquist-Estabrook [H.D.Wahlquist and F.B.Estabrook,J.Math.Phys.16 (1975) 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system.Based on the obtained prolongation structure,a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed.A Lie-Algebra representation of some hidden structural symmetries of the previous system,its Bcklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived.In the wake of the previous results,we extend the above prolongation scheme to higher-dimensional systems from which a new (2 + 1)-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation,which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention. 相似文献