452 research outputs found
The coupled modified nonlinear Schr\"{o}dinger equations on the half-line via the Fokas method
Coupled modified nonlinear Schr\"{o}dinger(CMNLS) equations describe the
pulse propagation in the picosecond or femtosecond regime of the birefringent
optical fibers. In this paper, we use the Fokas method to analyze the
initial-boundary value problem for the CMNLS equations on the half-line. Assume
that the solution u(x,t) and v(x,t) of CMNLS equations are exists, and we show
that it can be expressed in terms of the unique solution of a matrix
Riemann-Hilbert problem formulated in the plane of the complex spectral
parameter {\lambda}.Comment: 17 pages, 2 figure
The coupled Fokas-Lenells equations by a Riemann-Hilbert approach
In this paper, we use the unified transform method to consider the
initial-boundary value problem for the coupled Fokas-Lenells equations on the
half-line, assuming that the solution of the coupled
Fokas-Lenells equations exists, we show that can be
expressed in terms of the unique solution of a matrix Riemann-Hilbert problem
formulated in the plane of the complex spectral parameter . Thus, the
solution can be obtained by integration with respect to
.Comment: 18 pages, 2 figures. arXiv admin note: substantial text overlap with
arXiv:1704.0362
A Riemann-Hilbert Approach to the Complex Sharma-Tasso-Olver Equation on the Half Line
In this paper, we use the Fokas method to analyze the complex
Sharma-Tasso-Olver(cSTO) equation on the half line. We show that it can be
represented in terms of the solution of a matrix RHP formulated in the plane of
the complex spectral parameter {\lambda}.Comment: arXiv admin note: text overlap with arXiv:1109.4935, arXiv:1205.1559,
arXiv:0808.1534 by other author
The Novel Symmetry Constraint and Binary Nonlinearization of the Super Generalized Broer-Kaup Hierarchy with Self-consistent Sources and Conservation Laws
The super generalized Broer-Kaup(gBK) hierarchy and its super Hamiltonian
structure are established based on a loop super Lie algebra and super-trace
identity. Then the self-consistent sources, the conservation laws, the novel
symmetry constraint and the binary nonlinearization of the super gBK hierarchy
are generated, respectively. In addition, the integrals of motion required for
Liouville integrability are explicitly given.Comment: 19 pages, 0 figure
An integrable generalization of the super Kaup-Newell soliton hierarchy and its bi-Hamiltonian structure
An integrable generalization of the super Kaup-Newell(KN) isospectral problem
is introduced and its corresponding generalized super KN soliton hierarchy are
established based on a Lie super-algebra B(0,1) and super-trace identity in
this paper. And the resulting super soliton hierarchy can be put into a super
bi-Hamiltonian form. In addition, a generalized super KN soliton hierarchy with
self-consistent sources is also presented.Comment: 12 page
An initial-boundary value problem for the coupled focusing-defocusing complex short pulse equation with a Lax pair
In this paper we investigate the coupled focusing-defocusing complex short
pulse equation, which describe the propagation of ultra-short optical pulses in
cubic nonlinear media. Through the unified transform method, the
initial-boundary value problem for the coupled focusing-defocusing complex
short pulse equation with Lax pair on the half-line are to be
analyzed. Assuming that the solution of the coupled
focusing-defocusing complex short pulse equation exists, we show that
can be expressed in terms of the unique
solution of a matrix Riemann-Hilbert problem formulated in the
complex -plane. Thus, the solution can be
obtained by integration with respect to . Moreover, we also get that some
spectral functions are not independent and satisfy the so-called global
relation.Comment: 20 pages, 4 figures. arXiv admin note: text overlap with
arXiv:1704.0362
Riemann-Hilbert approach for a mixed coupled nonlinear Schr\"odinger system and its soliton solutions
In this work, we examine the integrable mixed coupled nonlinear Schr\"odinger
(mCNLS) system, which describe the propagation of an optical pulse in a
birefringent optical fiber. By the Riemann-Hilbert(RH) approach, the N-soliton
solutions of the mCNLS system can be expressed explicitly when the jump matrix
of a specific RH problem is a unit matrix. As a special example, the
expression of one- and two-soliton are displayed explicitly. More generally, as
a promotion, an integrable generalized multi-component NLS system with its
linear spectral problem be discussed. It is hoped that our results can help
enrich the nonlinear dynamical behaviors of the mCNLS.Comment: 15 pages, 1 figures. arXiv admin note: text overlap with
arXiv:1809.0703
The initial-boundary value problems for the coupled derivative nonlinear Schr\"odinger equations on the half-line
The unified transform method is used to analyze the initial-boundary value
problem for the coupled derivative nonlinear Schr\"odinger(CDNLS) equations on
the half-line. In this paper, we assume that the solution and
of CDNLS equations are exists, and we show that it can be expressed in terms of
the unique solution of a matrix Riemann-Hilbert problem formulated in the plane
of the complex spectral parameter .Comment: arXiv admin note: substantial text overlap with arXiv:1704.03623,
arXiv:1712.06449, arXiv:1711.0386
On the Riemann-Hilbert problem for the Chen-Lee-Liu derivative nonlinear Schr\"{o}dinger equation
In this work, we investigated a combined Chen-Lee-Liu derivative nonlinear
Schr\"{o}dinger equation(called CLL-NLS equation by Kundu) on the half-line by
unified transformation approach. We gives spectral analysis of the Lax pair for
CLL-NLS equation, and establish a matrix Riemann-Hilbert problem, so as to
reconstruct the solution of the CLL-NLS equation by solving.
Furthermore, the spectral functions are not independent, but enjoy by a
compatibility condition, which is the so-called global relation
Riemann-Hilbert method and N-soliton solutions for the mixed Chen-Lee-Liu derivative nonlinear Schr\"{o}dinger equation
In this paper, we aim to investigate the mixed Chen-Lee-Liu derivative
nonlinear Schr\"{o}dinger(CLL-NLS) equation via the Riemann-Hilbert(RH) method.
we construct a RH problem base on the Jost solution of the Lax pair. By solving
this RH problem corresponding to the non reflection case, the N-soliton
solution of CLL-NLS equation is obtained, which expression is the ratio of
determinant and determinant
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