[PDF] Top 20 A novel nonlinear evolution equation integrable by the inverse scattering method
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A novel nonlinear evolution equation integrable by the inverse scattering method
... the inverse scattering transform (IST) method. This equation arose as a result describing the high-frequency perturbations in a relaxing ...Hirota’s method and the IST method are ... See full document
8
The quench map in an integrable classical field theory: nonlinear Schrödinger equation
... with dµ ∗ (−k ∗ ) = dλ(k). This special relation comes from the fact that both q and q ∗ appear in NLSE. Rosales then shows that this series can be resummed for not necessarily small values of ε and in particular one can ... See full document
37
On the Inverse Scattering Method for Integrable PDEs on a Star Graph
... now, integrable partial differential equations (PDEs), and more generally integrable systems, have fuelled research and important discoveries in Mathematics and Physics, and still ...of integrable ... See full document
27
The Quench Map in an Integrable Classical Field Theory: Nonlinear Schrödinger Equation
... the scattering data is simply to change the number of zeros in the spectral function a(k), while maintaining its rational form and the reflectionless property b(k) = ...fixed-c scattering data associated to ... See full document
35
On the Inverse Scattering Method for Integrable PDEs on a Star Graph
... now, integrable partial differential equations (PDEs), and more generally integrable systems, have fuelled research and important discoveries in Mathematics and Physics, and still ...of integrable ... See full document
20
Traveling Wave Solutions of Nonlinear Evolution Equations Via the New Generalized (G′/G) Expansion Method
... of nonlinear physical ...of nonlinear equations still have drawn a lot of interest by diverse group of ...balance method [1], the tanh-function method [2], the extended tanh-function ... See full document
8
Lagrangian and Hamiltonian structures in an integrable hierarchy and space–time duality
... the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) ...each integrable nonlinear evolution equation (NLEE) in the hierarchy, ... See full document
25
Polynomial bundles and generalised Fourier transforms for integrable equations on A.III-type symmetric spaces
... The construction of the recursion operator for Lax operators, whose explicit dependence on the spectral parameter λ is comparatively simple (say, linear, or quadratic) was done a long time ago [1, 27, 15, 16]. ... See full document
49
Lagrangian and Hamiltonian structures in an integrable hierarchy and space-time duality
... the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) ...each integrable nonlinear evolution equation (NLEE) in the hierarchy, ... See full document
26
On a systematic approach to defects in classical integrable field theories
... systematic method on several well-known examples of integrable nonlinear ...the method to another inverse scattering method scheme, the Kaup-Newell scheme [17], which ... See full document
27
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... KdV equation and the spectral theory for the Sturm-Liouville operator on the ...the inverse scattering ...important nonlinear evolution equation, the so-called nonlinear ... See full document
11
Exact Solutions of the BBM and MBBM Equations by the Generalized (G'/G )-expansion Method Equations
... of nonlinear partial differential equations in modelling physical phenomena has become an important ...the inverse scattering transform[1], Hirot a’s bilinear method[2], sine-cosine ... See full document
5
Inverse Scattering of a Conducting Cylinder in Free Space by Modified Fireworks Algorithm
... the inverse scattering of a conducting cylinder is given by modified fireworks ...direct scattering is formulated as an integral equation, which contains the target shape ...The ... See full document
12
Factorization in integrable systems with impurity
... quantum inverse scattering method applied to the nonlinear Schr¨odinger equation with impurity [19], which constitutes the first known example of this kind, and in the investigation of ... See full document
9
On a direct construction of inverse scattering problems for integrable nonlinear evolution equations in the two spatial dimension
... a method to construct inverse scattering problems for integrable nonlinear evo- lution equations in the two-spatial ...linearized equation and the spatial component is a partial ... See full document
12
Yang-Baxter and reflection maps from vector solitons with a boundary
... the inverse scattering method of the vector nonlinear Schrödinger equation with integrable boundary con- ditions, we discuss the factorization of the interactions of N -soliton ... See full document
30
Yang–Baxter and reflection maps from vector solitons with a boundary
... the inverse scattering method of the vector nonlinear Schrödinger equation with integrable boundary con- ditions, we discuss the factorization of the interactions of N -soliton ... See full document
30
Controllability for nonlinear evolution equations with monotone operators
... For the theory of monotone operators, there are many literature works; for example, see Lions [], Stampacchia [], Browder [], and the references cited therein. Kenmochi [] derived new results on monotone operator ... See full document
17
Continuous dependence on data for a solution of the quasilinear parabolic equation with a periodic boundary condition
... In this study we prove the continuous dependence of the solution u = u(x, t) upon the data ϕ(x) and f (x, t, u). In [], a similar iteration method is used with this kind of a local boundary condition for a ... See full document
6
A Equation and Its Connections to Nonlinear Integrable System
... c relates the system (5) to a solvable yet still nonlinear system. Interestingly, a system similar to (6) arises ([10] [11]) if one seeks potentials for which the large frequency WKB series is finite and yields ... See full document
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