共查询到20条相似文献,搜索用时 15 毫秒
1.
V. A. Arkad'ev A. K. Pogrebkov M. K. Polivanov 《Journal of Mathematical Sciences》1985,31(6):3264-3279
The paper is devoted to the construction of singular solutions of the KdV equation. The presentation is based on a variant of the inverse scattering method for singular solutions of nonlinear equations developed in previous works of the authors.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 133, pp. 17–37, 1984.In conclusion we wish to express our gratitude to F. Calogero, who drew our attention to works [4–6], an to mention that the generalization of these works proposed here is based on the early paper [13] of L. D. Faddeev. 相似文献
2.
A hierarchy of the inverse KdV equation is discussed. Through the bilinear form of Lax pairs, we prove a generalized Darboux-Crum theorem of the hierarchy. The Bäcklund transformation and the generalized Wronskian solutions are presented. The soliton solutions, explicit rational solutions are obtained then. 相似文献
3.
《Chaos, solitons, and fractals》2001,12(12):2283-2293
In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the nonlinear dispersive KdV equation with initial profile. The approach rests mainly on Adomian decomposition method. The single soliton, the two-soliton and rational solutions are obtained by this method. Numerical examples are tested to illustrate the pertinent feature of the proposed algorithm. 相似文献
4.
《Chaos, solitons, and fractals》2005,23(2):651-655
Construction of a type of simple loop algebra is devoted to establishing an isospectral problem. It follows that the multi-component KdV hierarchy of soliton equations is obtained. Further, an expanded loop algebra of the above algebra is presented, which is used to work out the multi-component integrable coupling system of the multi-component KdV hierarchy. 相似文献
5.
We study special polynomials used to represent rational solutions of the hierarchy of the second Painlevé equation. We find
several recursion relations satisfied by these polynomials. In particular, we obtain a differential-difference relation that
allows finding any polynomial recursively. This relation is an analogue of the Toda chain equations.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 1, pp. 58–67, October, 2007. 相似文献
6.
A new super-extension of the KdV hierarchy is proposed, which is associated with a 3×3 matrix spectral problem. Using super-trace identity, generalized bi-Hamiltonian structures of this hierarchy are established. Moreover, infinite conservation laws of the new super-KdV equation are derived. 相似文献
7.
Doklady Mathematics - A relationship between the continued fraction expansion of the quadratic irrationalities of hyperelliptic fields and the Mumford polynomials determining addition in the group... 相似文献
8.
Theoretical and Mathematical Physics - Based on the high-order restricted flows of the extended fifth-order KdV (efKdV) equation, the efKdV equation with self-consistent sources (efKdVESCS) is... 相似文献
9.
M. N. B. Mohamad 《Mathematical Methods in the Applied Sciences》1992,15(2):73-78
This paper presents two different methods for the construction of exact solutions to the combined KdV and mKdV equation. The first method is a direct one based on a general form of solution to both the KdV and the modified KdV (mKdV) equations. The second method is a leading order analysis method. The method was devised by Jeffrey and Xu. Each of these methods is capable of solving the combined KdV and mKdV equation exactly. 相似文献
10.
A. M. Zeitlin 《Theoretical and Mathematical Physics》2006,147(2):698-708
We continue the study of the quantization of supersymmetric integrable KdV hierarchies. We consider the N=2 KdV model based
on the sl(1)(2|1) affine algebra but with a new algebraic construction for the L-operator, different from the standard Drinfeld-Sokolov
reduction. We construct the quantum monodromy matrix satisfying a special version of the reflection equation and show that
in the classical limit, this object precisely gives the monodromy matrix of the N=2 supersymmetric KdV system. We also show
that at both the classical and the quantum levels, the trace of the monodromy matrix (transfer matrix) is invariant under
two supersymmetry transformations and the zero mode of the associated U(1) current.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 303–314, May, 2006. 相似文献
11.
《Communications in Nonlinear Science & Numerical Simulation》2008,13(9):1776-1781
By using some exact solutions of an auxiliary ordinary differential equation, a new direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the complex coupled KdV equations and modified KdV equation. New exact complex solutions are obtained. 相似文献
12.
《Communications in Nonlinear Science & Numerical Simulation》2008,13(2):331-339
In this work we introduce new schemes, each combines two hyperbolic functions, to study the KdV, mKdV, and the generalized KdV equations. It is shown that this class of equations gives conventional solitons and periodic solutions. We also show that the proposed schemes develop sets of entirely new solitary wave solutions in addition to the traditional solutions. The analysis can be used to a wide class of nonlinear evolutions equations. 相似文献
13.
Alvaro H. Salas 《Nonlinear Analysis: Real World Applications》2011,12(2):1314-1320
In this paper a special forced Korteweg–de Vries (KdV) equation is considered. This equation is established by recent studies as a simple mathematical model of describing the physics of a shallow layer of fluid subject to external forcing. It serves as an analytical model of tsunami generation by submarine landslides. The bilinear form for this equation is obtained with the aid of Hirota’s method. Some of its one-, two- and three-soliton as well as breather-type soliton solutions and other interesting solutions are derived. 相似文献
14.
15.
This paper presents a mapping approach for the construction of exact solutions to the combined KdV and mKdV equation. There exist two types of soliton solutions which will reduce back to those of the KdV and mKdV equations in some appropriate limits. Four types of the general cnoidal wave solutions are also obtained. 相似文献
16.
Luiz Gustavo Farah 《Journal of Differential Equations》2010,249(8):1968-1985
We prove that the initial value problem (IVP) for the critical generalized KdV equation ut+uxxx+x(u5)=0 on the real line is globally well-posed in Hs(R) if s>3/5 with the appropriate smallness assumption on the initial data. 相似文献
17.
Z. Kharebava 《Journal of Mathematical Sciences》2008,152(3):330-371
Rational homotopy types of simply connected topological spaces have been classified by weak equivalence classes of commutative
cochain algebras (Sullivan) and by isomorphism classes of minimal commutative A
∞-algebras (Kadeishvili).
We classify rational homotopy types of the space X by using the (noncommutative) singular cochain complex C*(X, Q), with additional structure given by the homotopies introduced by Baues, {E
1,k
} and {F
p,q}. We show that if we modify the resulting B
∞-algebra structure on this algebra by requiring that its bar construction be a Hopf algebra up to a homotopy, then weak equivalence
classes of such algebras classify rational homotopy types.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 43, Topology
and Its Applications, 2006. 相似文献
18.
Under three kinds of constraints of potential for KdV hierarchy,the two systems, stemming from the spatial part and the time part of the Lax pair for KdV hierarchy, are shown to be naturally consistent. For the former system, the constants of the motion are presented and the Painlevé property is examined.Project Supported by the National Natural Science Foundation of China. 相似文献
19.
A. O. Smirnov 《Acta Appl Math》1994,36(1-2):125-166
A method is proposed for constructing finite-gap elliptic inx or/and int solutions of the Korteweg-de Vries equation. Dynamics of poles for two-gap elliptic solutions of the KdV equation are considered. Numerous examples of new elliptic solutions of the KdV equation are given.Dedicated to the memory of J.-L. Verdier 相似文献
20.
Abdul‐Majid Wazwaz 《Numerical Methods for Partial Differential Equations》2007,23(2):247-255
In this work, the sine‐cosine method, the tanh method, and specific schemes that involve hyperbolic functions are used to study solitons and periodic solutions governed by the generalized KdV equation. New solutions are determined by using the hyperbolic functions schemes. The study introduces new approaches to handle nonlinear PDEs in the solitary wave theory. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 247–255, 2007 相似文献