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Bi-Integrable and Tri-Integrable Couplings of a Soliton Hierarchy Associated with SO(3)
Advances in Mathematical Physics, 2017 Based on the three-dimensional real special orthogonal Lie algebra SO(3), by zero curvature equation, we present bi-integrable and tri-integrable couplings associated with SO(3) for a hierarchy from the enlarged matrix spectral problems and the enlarged ...
Jian Zhang, Chiping Zhang, Yunan Cui
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Characters of Explicit Solutions for a Semidiscrete Integrable Coupled Equation
Advances in Mathematical Physics, 2021 A semidiscrete integrable coupled system is obtained by embedding a free function into the discrete zero-curvature equation. Then, explicit solutions of the first two nontrivial equations in this system are derived directly by the Darboux transformation ...
Qiulan Zhao, Qianqian Yang, Xiangwen Qu
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Zero-Curvature Solutions of the One-Dimensional Schrödinger Equation
Physica Scripta, 2005 We discuss special k=sqrt{2m(E-V(x))/\hbar^2}=0 (i. e. zero-curvature) solutions of the one-dimensional Schrodinger equation in several model systems which have been used as idealized versions of various quantum well structures. We consider infinite well plus Dirac delta function cases (where E=V(x)=0) and piecewise-constant potentials, such as ...
Belloni, M. +2 more
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Soliton surfaces via a zero-curvature representation of differential equations [PDF]
Journal of Physics A: Mathematical and Theoretical, 2012 28 pages, 2 ...
Grundland, A. M., Post, S.
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Geodesic path planning characteristics of the reconfigurable 1-S robot workspaces for hyperbolic, elliptical, and Euclidean geometries [PDF]
Archives of Control SciencesThe path-planning strategies are implemented by establishing the Riemann curvature tensor and geodesic equations of the 1-S robot workspace. This paper’s originality lies in formulation of the parametric 1-S robotworkspace for path planning, which is ...
Haydar Sahin
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Fractal and Fractional, 2021 The coupled cubic-quintic nonlinear Schrödinger (CQNLS) equation is a universal mathematical model describing many physical situations, such as nonlinear optics and Bose–Einstein condensate.
Huanhe Dong +4 more
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, 2014 In this paper, I derive a zero curvature representation of quantum Painlevé II equation and its Riccati form which can be reduced to the classical Painlevé II when ħ→0.
Mahmood, Irfan
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Rigid Levi degenerate hypersurfaces with vanishing CR-curvature
, 2022 We continue the study, initiated in our earlier article, of a class of rigid hypersurfaces in that are 2-nondegenerate and uniformly Levi degenerate of rank 1, having zero CR-curvature. We drop the restrictive assumptions of the earlier paper and give a
Isaev, Alexander
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A Higher-Order Energy Expansion to Two-Dimensional Singularly Neumann Problems [PDF]
, 2005 Of concern is the following singularly perturbed semilinear elliptic problem \begin{equation*} \left\{ \begin{array}{c} \mbox{${\epsilon}^2\Delta u -u+u^p =0$ in $\Omega$}\\ \mbox{$u>0$ in $\Omega$ and $
Yeung, W-K, Winter, M, Wei, J
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Binary Nonlinearization for AKNS-KN Coupling System
Abstract and Applied Analysis, 2014 The AKNS-KN coupling system is obtained on the base of zero curvature equation by enlarging the spectral equation. Under the Bargmann symmetry constraint, the AKNS-KN coupling system is decomposed into two integrable Hamiltonian systems with the ...
Xiangrong Wang, Xiaoen Zhang, Peiyi Zhao
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