共查询到20条相似文献,搜索用时 937 毫秒
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Solitons and Breathers of Electromagnetic Wave in Superlattices 总被引:4,自引:0,他引:4
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The algebraic mapping relations between the (2+1)-dimensional double sine-Gordon equation and the cubic nonlinear Klein—Gordon equation are constructed. Many new types of two-dimensional resonant kink, bright soliton and solitoff solutions are obtained, such as broken line shape, "V" shape, "snake" shape and "M" shape solitary waves, Zigzag-curve type, "ω" shape, peroidic-curve type, oscillatory Arch-type and parabolic shape bright soliton waves. We also investigate the propagating properties of some soliton solutions. 相似文献
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Amal K. Das 《Solid State Communications》1978,27(12):1445-1447
The solution of the sine-Gordon equation for a medium is studied in a simplified “quasi-linear” approximation. Several aspects of this approximation are explored and compared with other approximate solutions for the sine-Gordon soliton. 相似文献
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In this paper, we obtain the soliton solutions for the "good" Boussinesq equation on a constant background. Based on the asymptotic analysis of the solutions, we find that this equation admits both the elastic and resonant soliton interactions, as well as various partially inelastic interactions comprised of such two fundamental interactions. Via picture drawing, we present some examples of soliton interactions on nonzero backgrounds. Our results enrich the knowledge of soliton interactions in the (1+1)-dimensional integrable equation with a single field. 相似文献
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Kai Drühl 《Physica D: Nonlinear Phenomena》1986,20(2-3):429-434
We study the propagation of real Raman solitons in the presence of collisional coherence decay by using Kaup's formulation on asymptotic perturbation theory and the symmetry properties of the related sine-Gordon equation. Neglecting the continuous spectrum the soliton parameters are calculated both to first order and to all orders in the coupling constant. Numerical results confirm the validity of the latter results. 相似文献
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This paper develops a new complex Hamiltonian structure forn-soliton solutions for a class of integrable equations such as the nonlinear Schrödinger, sine-Gordon and Korteweg-de Vries hierarchies of equations that yields, amongst other things, geometric phases in the sense of Hannay and Berry. For example, one of the possible soliton geometric phases is manifested by the well known phase shift that occurs for interacting solitons. The main new tools are complex angle representations that linearize the corresponding Hamiltonian flows on associated noncompact Jacobi varieties. This new structure is obtained by taking appropriate limits of the differential equations describing the class of quasi-periodic solutions. A method of asymptotic reduction of the angle representations is introduced for investigating soliton geometric phases that are related to the presence of monodromy at singularities in the space of parameters. In particular, the phase shift of interacting solitons can be expressed as an integral over a cycle on an associated Riemann surface. In this setting, soliton geometric asymptotics are constructed for studying geometric phases in the quantum case. The general approach is worked out in detail for the three specific hierarchies of equations mentioned. Some links with -functions, the braid group and geometric quantization are pointed out as well.Communicated by A. Jaffe 相似文献
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A general approach is given to obtain the system of ordinary differential equations which determines the pure soliton solutions for the class of generalized Korteweg-de Vries equations (cf. [6]). This approach also leads to a system of ordinary differential equations for the pure soliton solutions of the sine-Gordon equation. 相似文献
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Starting from n line soliton solutions of an integrable (2+1)-dimensional sine-Gordon system, one can find a dromion solution which is localized in all directions for a suitable potential. The dromion structures for a special (2+1)-dimensional sine-Gordon equation are studied in detail. The interactions among dromions are not elastic. In addition to a phase shift, the "shape" and the velocity of these dromions may also be changed after interaction. 相似文献
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In this paper, based on a Riemann theta function and Hirota's bilinear form, a straightforward way is presented to explicitly construct Riemann theta functions periodic waves solutions of the isospectral BKP equation.Once the bilinear form of an equation obtained, its periodic wave solutions can be directly obtained by means of an unified theta function formula and the way of obtaining the bilinear form is given in this paper. Based on this, the Riemann theta function periodic wave solutions and soliton solutions are presented. The relations between the periodic wave solutions and soliton solutions are strictly established and asymptotic behaviors of the Riemann theta function periodic waves are analyzed by a limiting procedure. The N-soliton solutions of isospectral BKP equation are presented with its detailed proof. 相似文献
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In this paper, based on a Riemann theta function and Hirota's bilinear form, a straightforward way is presented to explicitly construct Riemann theta functions periodic waves solutions of the isospectral BKP equation. Once the bilinear form of an equation obtained, its periodic wave solutions can be directly obtained by means of an unified theta function formula and the way of obtaining the bilinear form is given in this paper. Based on this, the Riemann theta function periodic wave solutions and soliton solutions are presented. The relations between the periodic wave solutions and soliton solutions are strictly established and asymptotic behaviors of the Riemann theta function periodic waves are analyzed by a limiting procedure. The N-soliton solutions of isospectral BKP equation are presented with its detailed proof. 相似文献
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Quantitative analysis of soliton interactions based on the exact solutions of the nonlinear Schrödinger equation 下载免费PDF全文
Xuefeng Zhang 《中国物理 B》2023,32(1):10505-010505
We make a quantitative study on the soliton interactions in the nonlinear Schrödinger equation (NLSE) and its variable-coefficient (vc) counterpart. For the regular two-soliton and double-pole solutions of the NLSE, we employ the asymptotic analysis method to obtain the expressions of asymptotic solitons, and analyze the interaction properties based on the soliton physical quantities (especially the soliton accelerations and interaction forces); whereas for the bounded two-soliton solution, we numerically calculate the soliton center positions and accelerations, and discuss the soliton interaction scenarios in three typical bounded cases. Via some variable transformations, we also obtain the inhomogeneous regular two-soliton and double-pole solutions for the vcNLSE with an integrable condition. Based on the expressions of asymptotic solitons, we quantitatively study the two-soliton interactions with some inhomogeneous dispersion profiles, particularly discuss the influence of the variable dispersion function f(t) on the soliton interaction dynamics. 相似文献
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In this paper, multi-periodic (quasi-periodic) wave solutions are constructed for the Boiti-Leon-Manna-Pempinelli (BLMP) equation by using Hirotabilinear method and Riemann theta function. At the same time, weanalyze in details asymptotic properties of the multi-periodic wave solutions and give their asymptotic relations between the periodic wave solutions and the soliton solutions. 相似文献
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With the procedure to solve explicitly the equations of the Riemann matrix with poles, multisoliton solutions to the DNLS equation are found formally. A single soliton solution is given explicitly and the asymptotic behaviors of multisoliton solutions are discussed. 相似文献
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Huiqun Zhang 《Reports on Mathematical Physics》2007,60(1):97-106
A direct algebraic method is introduced for constructing exact travelling wave solutions of nonlinear partial differential equations with complex phases. The scheme is implemented for obtaining multiple soliton solutions of the generalized Zakharov equations, and then new exact travelling wave solutions with complex phases are obtained. In addition, by using new exact solutions of an auxiliary ordinary differential equation, new exact travelling wave solutions for the generalized Zakharov equations are obtained. 相似文献
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In this paper we introduce a few novel generalized sine-Gordon equations and study the dynamics of its solitons in inhomogeneous
media. We consider length, mass, gravitational acceleration and spring stiffness of a coupled pendulums chain as a function
of position x. Then in the continuum limit we derive semi-analytical and numerical soliton solutions of the modified sine-Gordon equation
in the inhomogeneous media. The obtained results confirm that the behavior of solitons in these media is similar to that of
a classical point particle moved in an external potential. 相似文献