共查询到20条相似文献,搜索用时 15 毫秒
1.
N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources and the hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scattering transform. 相似文献
2.
N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources and the hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scattering transform. 相似文献
3.
Iryna Egorova Johanna Michor Gerald Teschl 《Mathematical Physics, Analysis and Geometry》2013,16(2):111-136
We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second order difference operators) with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give necessary and sufficient conditions for the scattering data in the case of perturbations with finite second (or higher) moment. 相似文献
4.
Exact Two-Soliton Solutions for Discrete mKdV Equation 总被引:1,自引:0,他引:1
YANG Qin ZHANG Hai-Jun 《理论物理通讯》2008,49(6):1553-1556
An exact two-soliton solution of discrete mKdv equation is derived by using the Hirota direct approach. In addition, we plot the soliton solutions to discuss the properties of solitons. It is worth while noting that we obtain the completely elastic interaction between the two solitons. 相似文献
5.
An explicR N-fold Darboux transformation with multi-parameters for coupled mKdV equation is constructed with the help of a gauge transformation of the Ablowitz-Kaup-Newell-Segur (AKNS) system spectral problem. By using the Darboux transformation and the reduction technique, some multi-soliton solutions for the complex mKdV equation are obtained. 相似文献
6.
By the application of the extended tanh method and the symbolic computation
system Mathematica, new soliton-like
solutions are obtained for the combined KdV and mKdV (KdV-mKdV) equation. 相似文献
7.
Anne Boutet de Monvel Alexander Its Vladimir Kotlyarov 《Communications in Mathematical Physics》2009,290(2):479-522
We consider the focusing nonlinear Schrödinger equation on the quarter plane. The initial data are vanishing at infinity while the boundary data are time- periodic, of the form \({a{\rm e}^{\i\alpha} {\rm e}^{2\i\omega t}}\) . The goal of this paper is to study the asymptotic behavior of the solution of this initial-boundary-value problem. The main tool is the asymptotic analysis of an associated matrix Riemann–Hilbert problem. We show that for \({\omega < -3a^2}\) the solution of the IBV problem has different asymptotic behaviors in different regions. In the region \({x > 4bt}\) , where \({b\mathop{:=} \sqrt{(a^2-\omega)/2} > 0}\) , the solution takes the form of the Zakharov-Manakov vanishing asymptotics. In a region of type \({4bt-\frac{N+1}{2a} {\rm log} t < x < 4bt}\) , where N is any integer, the solution is asymptotic to a train of asymptotic solitons. In the region \({4(b-a\sqrt2)t < x < 4bt}\) , the solution takes the form of a modulated elliptic wave. In the region \({0 < x < 4(b-a\sqrt2)t}\) , the solution takes the form of a plane wave. 相似文献
8.
9.
In this paper, new Jacobi elliptic function solutions of
multi-component mKdV equation are obtained directly in a unified
way. When the modulus m→1, those periodic solutions
degenerate as the corresponding hyperbolic function solutions.
Then, to the three-component mKdV equation, five types of
effective solution are presented in detail. 相似文献
10.
We investigate integrable boundary conditions (BCs) for the principal chiral model on the half-line, and rational solutions of the boundary Yang-Baxter equation (BYBE). In each case we find a connection with (type I, Riemannian, globally) symmetric spaces G/H: there is a class of integrable BCs in which the boundary field is restricted to lie in a coset of H; these BCs are parametrized by G/H×G/H; there are rational solutions of the BYBE in the defining representations of all classical G parametrized by G/H; and using these we propose boundary S-matrices for the principal chiral model, parametrized by G/H×G/H, which correspond to our boundary conditions.An erratum to this article can be found at 相似文献
11.
YU Ya-Xuan WANG Qi ZHANG Hong-Qing 《理论物理通讯》2005,44(6):1011-1014
In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result, many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple. 相似文献
12.
Fabio Pusateri 《Communications in Mathematical Physics》2014,332(3):1203-1234
We consider the question of scattering for the boson star equation in three space dimensions. This is a semi-relativistic Klein-Gordon equation with a cubic nonlinearity of Hartree type. We combine weighted estimates, obtained by exploiting a special null structure present in the equation, and a refined asymptotic analysis performed in Fourier space, to obtain global solutions evolving from small and localized Cauchy data. We describe the behavior of such solutions at infinity by identifying a suitable nonlinear asymptotic correction to scattering. As a byproduct of the weighted energy estimates alone, we also obtain global existence and (linear) scattering for solutions of semi-relativistic Hartree equations with potentials decaying faster than Coulomb. 相似文献
13.
Bifurcation, bistability and solitary waves of the combined KdV and mKdV equation are investigated systematically. At first, bifurcation and bistability are analyzed by selecting an integral constant as the bifurcation parameter. Then, different
conditions expressed in terms of the bifurcation parameter are obtained for the existence of breather-like, algebraic, pulse-like solitary waves, and shock waves. All types of the solitary wave and shock wave solutions are given by direct integration. Finally, an approximate analytic method by employing the interpolation
polynomials is utilized to give simpler forms for the pulse-like solitary wave solutions. In view of the references, our results are the most complete and the theoretical methods are the simplest
hitherto. 相似文献
14.
HE Jing-Song CHEN Shi-Rong 《理论物理通讯》2005,44(8)
Hamiltonian formalism of the mKdV equation with non-vanishing boundary valueis re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved some questionable points [T.C. Au Yeung and P.C.W. Fung, J. Phys. A 21 (1988) 3575]. In this note, simple results are obtained in terms of an affine parameter and a Galileo transformation is introduced to ensure the results compatible with those derived from the inverse scattering transform. 相似文献
15.
HE Jing-Song CHEN Shi-Rong 《理论物理通讯》2005,44(2):321-325
Hamiltonian formalism of the mKdV equation with non-vanishing boundary value is re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved some questionable points [T.C. Au Yeung and P.C.W. Fung, J. Phys. A 21 (1988) 3575]. In this note, simple results are obtained in terms of an affine parameter and a Galileo transformation is introduced to ensure the results compatible with those derived from the inverse scattering transform. 相似文献
16.
17.
YU Ya-Xuan WANG Qi ZHANG Hong-Qing 《理论物理通讯》2005,44(12)
In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple. 相似文献
18.
New Exact Solutions to the Combined KdV and mKdV Equation 总被引:2,自引:0,他引:2
Yan-ze Peng 《International Journal of Theoretical Physics》2003,42(4):863-868
The modified mapping method is developed to obtain new exact solutions to the combined KdV and mKdV equation. The method is applicable to a large variety of nonlinear evolution equations, as long as odd- and even-order derivative terms do not coexist in the equation under consideration. 相似文献
19.
New Solitary Wave Solution of the Combined KdV and mKdV Equation 总被引:3,自引:0,他引:3
Jiefang Zhang 《International Journal of Theoretical Physics》1998,37(5):1541-1546
This paper presents two different methods forthe construction of new exact solitary wave solutions tothe combined KdV and mKdV equation. There exist 12 typesof soliton solutions which reduce to those of the mKdV equation. There exist three typesof solurion solutions which reduce to those of the KdVequation. 相似文献
20.
Boundary value problems for integrable nonlinear evolution PDEs, like the modified KdV equation, formulated on the half-line can be analyzed by the so-called unified transform method. For the modified KdV equation, this method yields the solution in terms of the solution of a matrix Riemann-Hilbert problem uniquely determined in terms of the initial datum q(x,0), as well as of the boundary values {q(0, t),qx(0, t),qxx(0, t)}. For the Dirichlet problem, it is necessary to characterize the unknown boundary values qx(0, t) and qxx(0, t) in terms of the given data q(x, 0) and q(0, t). It is shown here that in the particular case of a vanishing initial datum and of a sine wave as Dirichlet datum, qx(0, t) and qxx(0, t) can be computed explicitly at least up to third order in a perturbative expansion and that at least up to this order, these functions are asymptotically periodic for large t. 相似文献