Physics Letters A, ISSN 0375-9601, 2009, Volume 373, Issue 21, pp. 1844 - 1846

In this work, four ( 2 + 1 ) -dimensional nonlinear evolution equations, generated by the Jaulent–Miodek hierarchy, are investigated. The necessary condition...

Multiple kink solutions | Multiple singular kink solutions | Nonlinear [formula omitted]-dimensional equation | Hirota bilinear method | Nonlinear (2 + 1)-dimensional equation | HIROTA 3-SOLITON CONDITION | PHYSICS, MULTIDISCIPLINARY | BURGERS EQUATIONS | FRONT SOLUTIONS | SEARCH | Nonlinear (2+1)-dimensional equation | SHALLOW-WATER WAVES | EVOLUTION-EQUATIONS | TANH-COTH METHOD | KP EQUATION | BILINEAR EQUATIONS | N-SOLITON SOLUTION

Multiple kink solutions | Multiple singular kink solutions | Nonlinear [formula omitted]-dimensional equation | Hirota bilinear method | Nonlinear (2 + 1)-dimensional equation | HIROTA 3-SOLITON CONDITION | PHYSICS, MULTIDISCIPLINARY | BURGERS EQUATIONS | FRONT SOLUTIONS | SEARCH | Nonlinear (2+1)-dimensional equation | SHALLOW-WATER WAVES | EVOLUTION-EQUATIONS | TANH-COTH METHOD | KP EQUATION | BILINEAR EQUATIONS | N-SOLITON SOLUTION

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 04/2018, Volume 51, Issue 21

We establish a correspondence between rational solutions to the matrix KP hierarchy and the spin generalization of the Calogero-Moser system on the level of...

matrix KP hierarchy | Calogero-Moser hierarchy | pole dynamics | BODY PROBLEMS | PARTICLES | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI EQUATION | ELLIPTIC SOLUTIONS

matrix KP hierarchy | Calogero-Moser hierarchy | pole dynamics | BODY PROBLEMS | PARTICLES | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI EQUATION | ELLIPTIC SOLUTIONS

Journal Article

3.
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Kadomtsev–Petviashvili hierarchy: N-soliton solutions and distinct dispersion relations

Applied Mathematics Letters, ISSN 0893-9659, 02/2016, Volume 52, pp. 74 - 79

In this paper, we investigate the Kadomtsev–Petviashvili (KP) hierarchy that was recently derived. We use the simplified Hirota’s method to study two...

Multiple solitons | Dispersion relation | KP hierarchy | MATHEMATICS, APPLIED | EQUATION

Multiple solitons | Dispersion relation | KP hierarchy | MATHEMATICS, APPLIED | EQUATION

Journal Article

International Journal of Modern Physics A, ISSN 0217-751X, 09/2019, Volume 34, Issue 25, p. 1950142

Additional symmetry is an important kind of symmetries depending explicitly on the time and space variables, which can be expressed through Sato–Bäcklund...

Virasoro constraints | W-CONSTRAINTS | MODIFIED KP HIERARCHY | SQUARED EIGENFUNCTION SYMMETRIES | OPERATOR | PHYSICS, NUCLEAR | Sato-Backlund transformations | string equations | SOLITON-EQUATIONS | ADDITIONAL SYMMETRIES | VIRASORO | PHYSICS, PARTICLES & FIELDS

Virasoro constraints | W-CONSTRAINTS | MODIFIED KP HIERARCHY | SQUARED EIGENFUNCTION SYMMETRIES | OPERATOR | PHYSICS, NUCLEAR | Sato-Backlund transformations | string equations | SOLITON-EQUATIONS | ADDITIONAL SYMMETRIES | VIRASORO | PHYSICS, PARTICLES & FIELDS

Journal Article

Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 21, pp. 3819 - 3823

A method is proposed to construct a new extended KP hierarchy, which includes two types of KP equation with self-consistent sources and admits reductions to...

Extended KP hierarchy | KP equation with self-consistent sources | Lax representation | Gelfand–Dickey hierarchy with self-consistent sources | k-constrained KP hierarchy | Gelfand-Dickey hierarchy with self-consistent sources | PHYSICS, MULTIDISCIPLINARY | REPRESENTATION | extended KP hierarchy | SOLITON-EQUATIONS | SELF-CONSISTENT SOURCES | N-COMPONENT KP | TRANSFORMATIONS | Physics - Exactly Solvable and Integrable Systems

Extended KP hierarchy | KP equation with self-consistent sources | Lax representation | Gelfand–Dickey hierarchy with self-consistent sources | k-constrained KP hierarchy | Gelfand-Dickey hierarchy with self-consistent sources | PHYSICS, MULTIDISCIPLINARY | REPRESENTATION | extended KP hierarchy | SOLITON-EQUATIONS | SELF-CONSISTENT SOURCES | N-COMPONENT KP | TRANSFORMATIONS | Physics - Exactly Solvable and Integrable Systems

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 10/2014, Volume 47, Issue 39, pp. 392001 - 13

We show that the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) admits a suggestive reformulation through elliptic functions. We...

Löwner equation | integrable hierarchies | elliptic functions | BENNEY EQUATIONS | HODOGRAPH SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | KP HIERARCHY | PHYSICS, MATHEMATICAL | REDUCTIONS | POLYNOMIALS | STOCHASTIC LOEWNER EVOLUTION | PFAFF LATTICE | Lowner equation | MULTIPLY-CONNECTED DOMAINS | Functions (mathematics) | Reduction | Hierarchies | Elliptic functions | Mathematical analysis | Lattices

Löwner equation | integrable hierarchies | elliptic functions | BENNEY EQUATIONS | HODOGRAPH SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | KP HIERARCHY | PHYSICS, MATHEMATICAL | REDUCTIONS | POLYNOMIALS | STOCHASTIC LOEWNER EVOLUTION | PFAFF LATTICE | Lowner equation | MULTIPLY-CONNECTED DOMAINS | Functions (mathematics) | Reduction | Hierarchies | Elliptic functions | Mathematical analysis | Lattices

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 04/2015, Volume 48, Issue 19, pp. 1 - 20

We derive a particular solution of the extended r-reduced KP hierarchy, which is specified by a generalized string equation. The work is a generalization to...

Tau function | String equation | KP hierarchy | Wave function | tau function | PHYSICS, MULTIDISCIPLINARY | wave function | string equation | SPIN CURVES | PHYSICS, MATHEMATICAL | MODULI | Functions (mathematics) | Partitions | Hierarchies | Mathematical analysis | Strings

Tau function | String equation | KP hierarchy | Wave function | tau function | PHYSICS, MULTIDISCIPLINARY | wave function | string equation | SPIN CURVES | PHYSICS, MATHEMATICAL | MODULI | Functions (mathematics) | Partitions | Hierarchies | Mathematical analysis | Strings

Journal Article

Chinese Annals of Mathematics, Series B, ISSN 0252-9599, 5/2019, Volume 40, Issue 3, pp. 457 - 468

In this paper, the authors define the noncommutative constrained Kadomtsev-Petviashvili (KP) hierarchy and multi-component noncommutative constrained KP...

37K05 | Mathematics, general | Mathematics | 35Q53 | Applications of Mathematics | Multi-component noncommutative constrained KP hierarchy | Recursion operator | 37K10 | Noncommutative constrained KP hierarchy | MATHEMATICS

37K05 | Mathematics, general | Mathematics | 35Q53 | Applications of Mathematics | Multi-component noncommutative constrained KP hierarchy | Recursion operator | 37K10 | Noncommutative constrained KP hierarchy | MATHEMATICS

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 07/2015, Volume 76, pp. 10 - 23

In this paper, we construct the Sato theory including the Hirota bilinear equations and tau function of a new q-deformed Toda hierarchy (QTH). Meanwhile the...

DEFORMED KP HIERARCHY | EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

DEFORMED KP HIERARCHY | EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 01/2012, Volume 53, Issue 1, pp. 013517 - 013517-24

In this paper, we define Orlov-Schulman's operators M L , M R , and then use them to construct the additional symmetries of the bigraded Toda hierarchy. We...

REPRESENTATIONS | KP HIERARCHY | ALGEBRA | PHYSICS, MATHEMATICAL | ADDITIONAL SYMMETRIES | STRING EQUATION | BKP HIERARCHY

REPRESENTATIONS | KP HIERARCHY | ALGEBRA | PHYSICS, MATHEMATICAL | ADDITIONAL SYMMETRIES | STRING EQUATION | BKP HIERARCHY

Journal Article

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Quasideterminant solutions of the extended noncommutative Kadomtsev–Petviashvili hierarchy

Theoretical and Mathematical Physics, ISSN 0040-5779, 7/2017, Volume 192, Issue 1, pp. 982 - 999

We construct a nonauto Darboux transformation for the extended noncommutative Kadomtsev–Petviashvili (ncKP) hierarchy and consequently derive its...

Theoretical, Mathematical and Computational Physics | extended noncommutative KP hierarchy | direct verification | Applications of Mathematics | quasi-Wronskian solution | Physics | Darboux transformation | PHYSICS, MULTIDISCIPLINARY | KP EQUATION | PHYSICS, MATHEMATICAL

Theoretical, Mathematical and Computational Physics | extended noncommutative KP hierarchy | direct verification | Applications of Mathematics | quasi-Wronskian solution | Physics | Darboux transformation | PHYSICS, MULTIDISCIPLINARY | KP EQUATION | PHYSICS, MATHEMATICAL

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 02/2016, Volume 49, Issue 14, p. 145206

We find all formal solutions to the h-dependent KP hierarchy. They are characterized by certain Cauchy-like data. The solutions are found in the form of formal...

KP hierarchy | tau-function | integrable hierarchies | TODA HIERARCHY | EFFECTIVISATION | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | DISPERSIONLESS LIMIT | RIEMANN THEOREM | Hierarchies | Logarithms | Mathematical analysis | Combinatorial analysis

KP hierarchy | tau-function | integrable hierarchies | TODA HIERARCHY | EFFECTIVISATION | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | DISPERSIONLESS LIMIT | RIEMANN THEOREM | Hierarchies | Logarithms | Mathematical analysis | Combinatorial analysis

Journal Article

Theoretical and Mathematical Physics(Russian Federation), ISSN 0040-5779, 01/2019, Volume 198, Issue 1, pp. 48 - 68

Splitting the algebra Psd of pseudodifferential operators into the Lie subalgebra of all differential operators without a constant term and the Lie subalgebra...

pseudodifferential operator | (dual) oscillating function | Statistical and Nonlinear Physics | (dual) wave function | Mathematical Physics | Grassmannian | strict KP hierarchy | (dual) linearization | KP hierarchy | Theoretical, Mathematical and Computational Physics | Applications of Mathematics | Physics | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Algebra

pseudodifferential operator | (dual) oscillating function | Statistical and Nonlinear Physics | (dual) wave function | Mathematical Physics | Grassmannian | strict KP hierarchy | (dual) linearization | KP hierarchy | Theoretical, Mathematical and Computational Physics | Applications of Mathematics | Physics | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Algebra

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2009, Volume 221, Issue 1, pp. 1 - 21

Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves....

Moduli spaces | ELSV formula | Witten's conjecture | KP hierarchy | Hurwitz numbers | MATHEMATICS

Moduli spaces | ELSV formula | Witten's conjecture | KP hierarchy | Hurwitz numbers | MATHEMATICS

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 05/2016, Volume 34, pp. 210 - 223

•By means of the gauge transformation, the Wronskian solutions of the DNLS equations have been given.•We have got the bright soliton and the dark-bright...

Gauge transformation | Constrained discrete KP hierarchy | Wronskian solution | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | KP HIERARCHY | GAUGE TRANSFORMATIONS | EQUATIONS | PHYSICS, MATHEMATICAL | ADDITIONAL SYMMETRIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | DETERMINANT REPRESENTATION | OPERATORS

Gauge transformation | Constrained discrete KP hierarchy | Wronskian solution | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | KP HIERARCHY | GAUGE TRANSFORMATIONS | EQUATIONS | PHYSICS, MATHEMATICAL | ADDITIONAL SYMMETRIES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | DETERMINANT REPRESENTATION | OPERATORS

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 11/2017, Volume 50, Issue 48, p. 485204

We consider multi-variable reductions of the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) in the elliptic parametrization. The...

dispersionlesss DKP hierarchy | Egorov type metric | GibbonsTsarev equation | elliptic Löwner equation | multi-variable reduction | BENNEY EQUATIONS | HODOGRAPH SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | KP HIERARCHY | INTEGRABLE HIERARCHIES | PHYSICS, MATHEMATICAL | elliptic Lowner equation | POLYNOMIALS | PFAFF LATTICE | LOEWNER THEORY | MATRIX INTEGRALS | SYSTEMS | HYDRODYNAMIC TYPE | Gibbons-Tsarev equation

dispersionlesss DKP hierarchy | Egorov type metric | GibbonsTsarev equation | elliptic Löwner equation | multi-variable reduction | BENNEY EQUATIONS | HODOGRAPH SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | KP HIERARCHY | INTEGRABLE HIERARCHIES | PHYSICS, MATHEMATICAL | elliptic Lowner equation | POLYNOMIALS | PFAFF LATTICE | LOEWNER THEORY | MATRIX INTEGRALS | SYSTEMS | HYDRODYNAMIC TYPE | Gibbons-Tsarev equation

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 04/2010, Volume 43, Issue 16, pp. 165202 - 165202

An extended Harry Dym hierarchy is constructed by using eigenfunctions and adjoint eigenfunctions of the spectral problems of the Harry Dym hierarchy...

SQUARED EIGENFUNCTION SYMMETRIES | BINARY CONSTRAINED FLOWS | PHYSICS, MULTIDISCIPLINARY | INTEGRABLE SYSTEMS | KP HIERARCHY | VARIABLES | SOLITON-EQUATIONS | WRONSKIAN SOLUTIONS | SEPARATION | PHYSICS, MATHEMATICAL | SELF-CONSISTENT SOURCES | KDV HIERARCHY | Operators | Construction | Hierarchies | Computation | Adjoints | Eigenfunctions | Mathematical models | Spectra

SQUARED EIGENFUNCTION SYMMETRIES | BINARY CONSTRAINED FLOWS | PHYSICS, MULTIDISCIPLINARY | INTEGRABLE SYSTEMS | KP HIERARCHY | VARIABLES | SOLITON-EQUATIONS | WRONSKIAN SOLUTIONS | SEPARATION | PHYSICS, MATHEMATICAL | SELF-CONSISTENT SOURCES | KDV HIERARCHY | Operators | Construction | Hierarchies | Computation | Adjoints | Eigenfunctions | Mathematical models | Spectra

Journal Article

Communications in Theoretical Physics, ISSN 0253-6102, 09/2016, Volume 66, Issue 3, pp. 263 - 268

Journal Article

Physical Review D - Particles, Fields, Gravitation and Cosmology, ISSN 1550-7998, 10/2015, Volume 92, Issue 8

In this paper three-dimensional higher spin theories in the Chern-Simons formulation with gauge algebra s1(N, R) are investigated which have Lifshitz symmetry...

ALGEBRAS | W-INFINITY | HAMILTONIAN-STRUCTURE | KP HIERARCHY | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Formulations | Gravitation | Algebra | Hierarchies | Cosmology | Formalism | Three dimensional | Symmetry

ALGEBRAS | W-INFINITY | HAMILTONIAN-STRUCTURE | KP HIERARCHY | ASTRONOMY & ASTROPHYSICS | PHYSICS, PARTICLES & FIELDS | Formulations | Gravitation | Algebra | Hierarchies | Cosmology | Formalism | Three dimensional | Symmetry

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 03/2019, Volume 137, pp. 76 - 86

In this paper, we construct the multicomponent modified KP hierarchy and its additional symmetries. The additional symmetries constitute an interesting...

Additional symmetries | Constrained multicomponent modified KP hierarchy | Multicomponent modified KP hierarchy | Quantum torus symmetries | Virasoro symmetry | MATHEMATICS | EQUATIONS | PHYSICS, MATHEMATICAL | Algebra

Additional symmetries | Constrained multicomponent modified KP hierarchy | Multicomponent modified KP hierarchy | Quantum torus symmetries | Virasoro symmetry | MATHEMATICS | EQUATIONS | PHYSICS, MATHEMATICAL | Algebra

Journal Article

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