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Symbolic software for soliton theory
 Also: Proc. of KdV '95 Conf
, 1995
"... program tests for the existence of solitons for nonlinear PDEs. It explicitly constructs solitons using Hirota’s bilinear method. In the second program, the Painlevé integrability test for ODEs and PDEs is implemented. The third program provides an algorithm to compute conserved densities for nonlin ..."
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Cited by 8 (5 self)
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for nonlinear evolution equations. The fourth software package aids in the computation of Lie symmetries of systems of differential and differencedifferential equations. Several examples illustrate the capabilities of the software. Key words: soliton theory, symbolic programs, Hirota method, Painlevé test, Lie
5 ISOMETRIC IMMERSIONS OF SPACE FORMS AND SOLITON THEORY
"... Isometric immersions of space forms and soliton theory ..."
Multidimensional Solitons – Theory
, 705
"... The onedimensional solitons described in Chapters II and III of this book can be extended into two and three dimensions. Such extensions are generally unstable [1]. However, in the tightly confined geometries associated with trapped BoseEinstein condensates (BECs) both bright and dark solitons ext ..."
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The onedimensional solitons described in Chapters II and III of this book can be extended into two and three dimensions. Such extensions are generally unstable [1]. However, in the tightly confined geometries associated with trapped BoseEinstein condensates (BECs) both bright and dark solitons
Reality problems in the soliton theory
, 2007
"... This is a survey article dedicated mostly to the theory of real regular finitegap (algebrogeometrical) periodic and quasiperiodic sineGordon solutions. Long period this theory remained unfinished and ineffective, and by that reason practically had no applications. Even for such simple physical q ..."
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This is a survey article dedicated mostly to the theory of real regular finitegap (algebrogeometrical) periodic and quasiperiodic sineGordon solutions. Long period this theory remained unfinished and ineffective, and by that reason practically had no applications. Even for such simple physical
BASIC ASPECTS OF SOLITON THEORY
, 2006
"... Abstract. This is a review of the main ideas of the inverse scattering method (ISM) for solving nonlinear evolution equations (NLEE), known as soliton equations. As a basic tool we use the fundamental analytic solutions χ ± (x, λ) of the Lax operator L(λ). Then the inverse scattering problem for L(λ ..."
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Abstract. This is a review of the main ideas of the inverse scattering method (ISM) for solving nonlinear evolution equations (NLEE), known as soliton equations. As a basic tool we use the fundamental analytic solutions χ ± (x, λ) of the Lax operator L(λ). Then the inverse scattering problem for L
Harmonic maps and soliton theory
 Mathematica Contemporanea
, 1992
"... The study of harmonic maps of a Riemann sphere into a Lie group or, more generally, a symmetric space has been the focus for intense research by a number of Differential Geometers and Theoretical Physicists. As a result, these maps are now quite well understood and are seen to correspond to holomorp ..."
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Cited by 6 (0 self)
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The study of harmonic maps of a Riemann sphere into a Lie group or, more generally, a symmetric space has been the focus for intense research by a number of Differential Geometers and Theoretical Physicists. As a result, these maps are now quite well understood and are seen to correspond to holomorphic maps into some (perhaps
7Multidimensional Solitons: Theory
"... The onedimensional solitons described in Parts II and III of this book can be extended into two and three dimensions. Such extensions are generally unstable [1]. However, in the tightly confined geometries associated with trapped Bose–Einstein condensates (BECs) both bright and dark solitons ..."
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The onedimensional solitons described in Parts II and III of this book can be extended into two and three dimensions. Such extensions are generally unstable [1]. However, in the tightly confined geometries associated with trapped Bose–Einstein condensates (BECs) both bright and dark solitons
The model equation of soliton theory
, 706
"... We consider an hierarchy of integrable 1 + 2dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on n arbitrary functions of one argument. The most interesting result is the simple equation for the generating function ..."
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of the hierarchy which defines the dynamics for the negative times and also has applications to the second order spectral problems. A rather general theory of integrable 1 + 1dimensional equations can be developed by study of polynomial solutions of this equation under condition of regularity of the corresponding
Laplacian growth and Whitham equations of soliton theory
 Physica D
, 2004
"... The Laplacian growth (the HeleShaw problem) of multiplyconnected domains in the limit of zero surface tension is proven to be equivalent to an integrable system of Whitham equations known in soliton theory. The Whitham equations describe slowly modulated periodic solutions of integrable hierarchie ..."
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Cited by 27 (5 self)
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The Laplacian growth (the HeleShaw problem) of multiplyconnected domains in the limit of zero surface tension is proven to be equivalent to an integrable system of Whitham equations known in soliton theory. The Whitham equations describe slowly modulated periodic solutions of integrable
Results 1  10
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25,952