Darboux transformation
N Fold Darboux transformation and solitonic interactions for a Volterra lattice system
... functions of space variables, and they are associated with complex eigenvalues of the as- sociated spectral problems []. It is worth pointing out that our results seem to be differ- ent from those reported in [] ...
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Darboux Transformation of Lax Pair for an Integrable Coupling of the Integrable Differential-Difference Equation
... gauge transformation of matrix spectral problems is called a Darboux transformation if it transforms the spectral problem into another spectral problem of the same ...a Darboux ...
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N Fold Darboux transformation of the discrete Ragnisco–Tu system
... At present, much work has been done on a single Darboux transformation (DT) of the Lax integrable nonlinear integrable systems [29–32]. Here we would like to construct an N -fold DT for the Ragnisco–Tu ...
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The general mixed nonlinear Schrödinger equation: Darboux transformation, rogue wave solutions, and modulation instability
... the Darboux transformation method [, ], the Bäcklund transformation [–], the Riemann-Hilbert formulation [–], the Hirota bilinear method [, ], Lie group analysis [], the similarity ...
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Semi Commutative Differential Operators Associated with the Dirac Opetator and Darboux Transformation
... In the present paper, the semi-commutative differential oparators associated with the 1-dimensional Dirac operator are constructed. Using this results, the hierarchy of the mKdV (−) polynomials are expressed in terms of ...
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N Fold Darboux Transformation for the Nonlocal Nonlinear Schrödinger (NNLS) Equation with the Self Induced PT Symmetric Potential
... [6] Guo, R., Tian, B. and Wang, L. (2012) Soliton Solutions for the Reduced Max- well-Bloch System in Nonlinear Optics via the n-Fold Darboux Transformation. Nonlinear Dynamics , 69, 2009-2020. ...
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Generalized Darboux Transformation and Rational Solutions for the Nonlocal Nonlinear Schrödinger Equation with the Self Induced Parity Time Symmetric Potential
... In this paper, I construct a generalized Darboux transformation for the nonlocal nonlinear Schrö- dinger equation with the self-induced parity-time symmetric potential. The N-order rational solu- tion is ...
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Darboux Transformation and New Multi Soliton Solutions of the Whitham Broer Kaup System
... variable transformation, the Whitham-Broer-Kaup system is transformed into a para- meter Levi ...N-fold Darboux trans- formation with multi-parameters is ...
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Darboux transformation for classical acoustic spectral problem
... For the Schrödinger operator, one of the most efficient ways of building potentials allowing exact solutions is the powerful and at the same time sim- ple formal method of factorization, or the Darboux ...
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Darboux transformation of the general Hirota equation: multisoliton solutions, breather solutions, and rogue wave solutions
... Darboux transformation (DT) technique is a method that can derive multisoliton so- lutions from trivial seed solutions in a purely algebraic procedure for the integrable non- linear wave equations ...gauge ...
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Darboux Transformation in the Tangent Squared Potential and Supersymmetry
... first-order Darboux transformation and the real valued condition of transformed potential for trigonometric tangent-squared potential ...between Darboux transformation and ...
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N Fold Darboux Transformation of the Jaulent Miodek Equation
... We study the exact solutions of the JM Equation 1.1 by using Darboux transformation DT, which is an effective method to get exact solutions from the trivial solutions of the nonlinear pa[r] ...
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N Fold Darboux Transformation for a Nonlinear Evolution Equation
... tering transformation (IST) [1], Bäcklund transformation [2], Darboux transformation [3], Painlevé analysis method [4], ...gauge transformation trans- forming a linear problem into ...
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Grassmann extensions of Yang-Baxter maps
... the Darboux transformation for the DNLS ...the Darboux matrices presented in section 3 and, from their associated refactorisation prob- lems, we construct ten-dimensional YB ...considered ...
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Darboux–Bäcklund transformations, dressing & impurities in multi-component NLS
... a Darboux transformation for the continuous vNLS equa- tions for both the focusing and defocusing ...the Darboux transformation, is structurally similar to the de- fect matrix as already ...
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Darboux Transforms and 2-Orthogonal Polynomials
... [7] F. A. Gr¨unbaum and L. Haine, ”Orthogonal polynomials satisfying differential equations: the role of the Darboux transformation”, in: D. Levi, L. Vinet, P. Winternitz (Eds.), Symmetries and ...
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Yang-Baxter maps and finite reduction groups with degenerated orbits
... Equations like the Lax-equation (9) are being met quite often in the area of integrable systems as, for instance, in the case of the Darboux transformations, where it represents the compatibility condition of the ...
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Darboux transformations with tetrahedral reduction group and related integrable systems
... In this paper we presented the Lax-Darboux scheme related to the tetrahedral reduction group. More precisely, we studied the Darboux transformations for the class of Lax operators which involve 3 × 3 ...
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Generalised Darboux-Koenigs Metrics and 3-Dimensional Superintegrable Systems
... The Darboux–Koenigs metrics in 2D are an important class of conformally flat, non-constant curvature metrics with a single Killing vector and a pair of quadratic Killing ...generalised Darboux–Koenigs ...
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Darboux Transformations and Fay Identities of the Extended Bigraded Toda Hierarchy.
... how Darboux transformations of the EBTH affect the tau- ...of Darboux transformations on the ...defined Darboux transformations on the wave functions for the ETH, and in [42], Li and Song generalized ...
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