Applied Mathematics and Computation, ISSN 0096-3003, 10/2018, Volume 335, pp. 12 - 24

The fundamental purpose of the present paper is to apply an effective numerical algorithm based on the mixture of homotopy analysis technique, Sumudu transform...

Drinfeld–Sokolov-–Wilson equation | Caputo fractional derivative | HASTM | Convergence analysis | SUMUDU TRANSFORM | MATHEMATICS, APPLIED | Drinfeld-Sokolov-Wilson equation | Water waves | Analysis | Algorithms

Drinfeld–Sokolov-–Wilson equation | Caputo fractional derivative | HASTM | Convergence analysis | SUMUDU TRANSFORM | MATHEMATICS, APPLIED | Drinfeld-Sokolov-Wilson equation | Water waves | Analysis | Algorithms

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2017, Volume 453, Issue 2, pp. 908 - 916

With the aid of Hamiltonian structures for the constrained modified KP flow, we show that a coupled Ramani equation is a bi-Hamiltonian system with a local...

Drinfeld–Sokolov hierarchy | Ramani equation | Hamiltonian structure | SYSTEM | MATHEMATICS | Drinfeld-Sokolov hierarchy | MATHEMATICS, APPLIED | INVERSE SCATTERING | SOLITON-SOLUTIONS | BACKLUND-TRANSFORMATIONS | Romani equation | LAX PAIRS | HIERARCHY

Drinfeld–Sokolov hierarchy | Ramani equation | Hamiltonian structure | SYSTEM | MATHEMATICS | Drinfeld-Sokolov hierarchy | MATHEMATICS, APPLIED | INVERSE SCATTERING | SOLITON-SOLUTIONS | BACKLUND-TRANSFORMATIONS | Romani equation | LAX PAIRS | HIERARCHY

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 05/2017, Volume 88, Issue 3, pp. 1869 - 1882

In the present article, the new exact solutions of time-fractional coupled Drinfeld-Sokolov-Wilson equations have been derived by using a new reliable...

Fractional complex transform | Time-fractional Drinfeld–Sokolov–Wilson equations | Jacobi elliptical function method | Local fractional calculus | MECHANICS | SOLITONS | COMPLEX TRANSFORM | Time-fractional Drinfeld-Sokolov-Wilson equations | ENGINEERING, MECHANICAL | Water waves | Differential equations | Differential calculus | Partial differential equations | Mathematical analysis | Exact solutions | Ordinary differential equations | Elliptic functions | Shallow water | Fractional calculus

Fractional complex transform | Time-fractional Drinfeld–Sokolov–Wilson equations | Jacobi elliptical function method | Local fractional calculus | MECHANICS | SOLITONS | COMPLEX TRANSFORM | Time-fractional Drinfeld-Sokolov-Wilson equations | ENGINEERING, MECHANICAL | Water waves | Differential equations | Differential calculus | Partial differential equations | Mathematical analysis | Exact solutions | Ordinary differential equations | Elliptic functions | Shallow water | Fractional calculus

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 11/2017, Volume 104, pp. 725 - 733

In this paper, the invariance properties of time fractional coupled Drinfeld–Sokolov–Satsuma–Hirota (DSSH) equations have been investigated using the Lie group...

New conservation laws | Erdélyi–Kober operator | Time fractional coupled Drinfeld–Sokolov–Satsuma–Hirota equations | Lie symmetry analysis | ORDER | Drinfeld-Sokolov-Satsuma-Hirota equations | BURGERS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | Time fractional coupled | PHYSICS, MATHEMATICAL | Erdelyi-Kober operator | Environmental law | Analysis

New conservation laws | Erdélyi–Kober operator | Time fractional coupled Drinfeld–Sokolov–Satsuma–Hirota equations | Lie symmetry analysis | ORDER | Drinfeld-Sokolov-Satsuma-Hirota equations | BURGERS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | Time fractional coupled | PHYSICS, MATHEMATICAL | Erdelyi-Kober operator | Environmental law | Analysis

Journal Article

Propulsion and Power Research, ISSN 2212-540X, 12/2018, Volume 7, Issue 4, pp. 320 - 328

In this article, the two variable -expansion method is suggested to investigate new and further general multiple exact wave solutions to the...

Soliton | Shallow water wave equation | Drinfeld-Sokolov-Satsuma-Hirota (DSSH) equation | Explicit wave solutions | Computer algebra software

Soliton | Shallow water wave equation | Drinfeld-Sokolov-Satsuma-Hirota (DSSH) equation | Explicit wave solutions | Computer algebra software

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2013, Volume 219, Issue 12, pp. 6473 - 6483

In this paper, we show that the recently developed formulation of the association between symmetries and conservation laws lead to double reductions of the...

Conservation laws | Drinfeld–Sokolov–Wilson equation | Lie symmetries | Double reduction | Korteweg–de Vries equation | Korteweg-de Vries equation | Drinfeld-Sokolov-Wilson equation | MATHEMATICS, APPLIED | CONSERVATION-LAWS | NONLOCAL SYMMETRIES | ASSOCIATION

Conservation laws | Drinfeld–Sokolov–Wilson equation | Lie symmetries | Double reduction | Korteweg–de Vries equation | Korteweg-de Vries equation | Drinfeld-Sokolov-Wilson equation | MATHEMATICS, APPLIED | CONSERVATION-LAWS | NONLOCAL SYMMETRIES | ASSOCIATION

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2017, Volume 2017, Issue 1, pp. 1 - 17

The symmetry analysis method is used to study the Drinfeld-Sokolov-Wilson system. The Lie point symmetries of this system are obtained. An optimal system of...

34A05 | 70S10 | 76M60 | Mathematics | Lie-Bäcklund symmetries | optimal system | Ordinary Differential Equations | conservation laws | explicit solutions | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Partial Differential Equations | Drinfeld-Sokolov-Wilson system | EXTENDED TANH-FUNCTION | MATHEMATICS, APPLIED | THEOREM | SIMPLEST EQUATION | DIFFERENTIAL-EQUATIONS | Lie-Backlund symmetries | REDUCTIONS | MATHEMATICS | ALGEBRAS | FLUID | WAVE-EQUATION | SOLITON | Conservation laws | Nonlinear equations | Partial differential equations | Nonlinear differential equations | Differential equations | Symmetry

34A05 | 70S10 | 76M60 | Mathematics | Lie-Bäcklund symmetries | optimal system | Ordinary Differential Equations | conservation laws | explicit solutions | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Partial Differential Equations | Drinfeld-Sokolov-Wilson system | EXTENDED TANH-FUNCTION | MATHEMATICS, APPLIED | THEOREM | SIMPLEST EQUATION | DIFFERENTIAL-EQUATIONS | Lie-Backlund symmetries | REDUCTIONS | MATHEMATICS | ALGEBRAS | FLUID | WAVE-EQUATION | SOLITON | Conservation laws | Nonlinear equations | Partial differential equations | Nonlinear differential equations | Differential equations | Symmetry

Journal Article

Results in Physics, ISSN 2211-3797, 12/2018, Volume 11, pp. 1161 - 1171

In this research work, we applying the modification form of extended auxiliary equation mapping method on three couple system of nonlinear ovulation equations...

Whitham-Broer-Kaup equation | Exact traveling wave solutions | Solitary wave solutions | Modified extended auxiliary equation mapping method | Drinfel’d-Sokolow-Wilson equation | The (2 + 1)-dimensional Broer-Kaup-Kupershmit equation | Drinfel'd-Sokolow-Wilson equation | DRINFELD-SOKOLOV-WILSON | PHYSICS, MULTIDISCIPLINARY | MODULATION INSTABILITY ANALYSIS | MATERIALS SCIENCE, MULTIDISCIPLINARY | SCHRODINGERS EQUATION | OPTICAL SOLITONS | WHITHAM-BROER-KAUP | 1ST INTEGRAL METHOD | HIGHER-ORDER | The (2 + 1)-dimensional Broer-Kaup-Kupershmit equation | CONSERVATION-LAWS | BRIGHT

Whitham-Broer-Kaup equation | Exact traveling wave solutions | Solitary wave solutions | Modified extended auxiliary equation mapping method | Drinfel’d-Sokolow-Wilson equation | The (2 + 1)-dimensional Broer-Kaup-Kupershmit equation | Drinfel'd-Sokolow-Wilson equation | DRINFELD-SOKOLOV-WILSON | PHYSICS, MULTIDISCIPLINARY | MODULATION INSTABILITY ANALYSIS | MATERIALS SCIENCE, MULTIDISCIPLINARY | SCHRODINGERS EQUATION | OPTICAL SOLITONS | WHITHAM-BROER-KAUP | 1ST INTEGRAL METHOD | HIGHER-ORDER | The (2 + 1)-dimensional Broer-Kaup-Kupershmit equation | CONSERVATION-LAWS | BRIGHT

Journal Article

Results in Physics, ISSN 2211-3797, 06/2019, Volume 13, p. 102263

In this paper the perturbed nonlinear Schrödinger equation (PNLSE) with power law nonlinearity in the medium of non-kerr is analyzed by employing Reccati...

Riccati equation mapping method | Soliton solutions | Periodic solutions | Solitary waves | Pertubed NLSE | DRINFELD-SOKOLOV-WILSON | EXPLICIT SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | DISPERSION | MATERIALS SCIENCE, MULTIDISCIPLINARY | WHITHAM-BROER-KAUP | TRAVELING-WAVE SOLUTIONS | STABILITY ANALYSIS | DISCRETE | ZAKHAROV-KUZNETSOV | WATER

Riccati equation mapping method | Soliton solutions | Periodic solutions | Solitary waves | Pertubed NLSE | DRINFELD-SOKOLOV-WILSON | EXPLICIT SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | DISPERSION | MATERIALS SCIENCE, MULTIDISCIPLINARY | WHITHAM-BROER-KAUP | TRAVELING-WAVE SOLUTIONS | STABILITY ANALYSIS | DISCRETE | ZAKHAROV-KUZNETSOV | WATER

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 11/2008, Volume 13, Issue 9, pp. 1748 - 1757

In this work, we establish exact solutions for coupled nonlinear evolution equations. The extended tanh method is used to construct solitary and soliton...

Drinfeld–Sokolov equation | (2 + 1)-Dimensional Konopelchenko–Dubrovsky equation | Coupled Hirota–Satsuma–KdV equation | Extended tanh method | (2 + 1)-Dimensional Konopelchenko-Dubrovsky equation | Coupled Hirota-Satsuma-KdV equation | Drinfeld-Sokolov equation | TRANSFORMATION | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | NONCOMPACT STRUCTURES | VARIANTS | SINE-COSINE METHOD | PHYSICS, FLUIDS & PLASMAS | SOLITONS SOLUTIONS | PHYSICS, MATHEMATICAL | COMPACT | extended tanh method | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | (2+1)-dimensional Konopelchenko-Dubrovsky equation | coupled Hirota-Satsuma-KdV equation | GENERALIZED FORMS | KDV

Drinfeld–Sokolov equation | (2 + 1)-Dimensional Konopelchenko–Dubrovsky equation | Coupled Hirota–Satsuma–KdV equation | Extended tanh method | (2 + 1)-Dimensional Konopelchenko-Dubrovsky equation | Coupled Hirota-Satsuma-KdV equation | Drinfeld-Sokolov equation | TRANSFORMATION | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | NONCOMPACT STRUCTURES | VARIANTS | SINE-COSINE METHOD | PHYSICS, FLUIDS & PLASMAS | SOLITONS SOLUTIONS | PHYSICS, MATHEMATICAL | COMPACT | extended tanh method | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | (2+1)-dimensional Konopelchenko-Dubrovsky equation | coupled Hirota-Satsuma-KdV equation | GENERALIZED FORMS | KDV

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 2014, Volume 1611, Issue 1, pp. 30 - 36

In this paper, the modified simple equation (MSE) method is used to construct exact solutions of the nonlinear Drinfeld-Sokolov system, Maccari system and...

Maccari system | Coupled Higgs equation | Nonlinear Drinfeld-Sokolov system | Modified simple equation method | Exact solutions | Nonlinear evolution equations | Applications of mathematics | Nonlinear systems | Solitary waves

Maccari system | Coupled Higgs equation | Nonlinear Drinfeld-Sokolov system | Modified simple equation method | Exact solutions | Nonlinear evolution equations | Applications of mathematics | Nonlinear systems | Solitary waves

Conference Proceeding

Transactions of the Moscow Mathematical Society, ISSN 0077-1554, 2016, Volume 77, pp. 203 - 246

We speak about the part of integrable system theory dealing with conformal theory and W-algebras (ordinary and deformed). Some new approaches to finding Bethe...

Quantum group | Drinfeld–Sokolov reduction | Integrable system | Bethe equations | Affine Lie algebra | Center at the critical level | Shuffle algebra

Quantum group | Drinfeld–Sokolov reduction | Integrable system | Bethe equations | Affine Lie algebra | Center at the critical level | Shuffle algebra

Journal Article

Chinese Journal of Physics, ISSN 0577-9073, 06/2017, Volume 55, Issue 3, pp. 780 - 797

In this paper, some new exact travelling wave solutions are constructed in different form of coupled partial differential equations having terms of odd and...

Jacobi elliptic solutions | Drinfel'd–Sokolov–Wilson equation | (2+1)-dimensional Broer–Kaup–Kupershmit equation | Modified extended direct algebraic method | Whitham–Broer–Kaup equation | Traveling wave solutions | SYSTEM | PHYSICS, MULTIDISCIPLINARY | Drinfel'd-Sokolov-Wilson equation | ION-ACOUSTIC-WAVES | ZAKHAROV-KUZNETSOV EQUATION | NONLINEAR SCHRODINGER-EQUATION | (2+1)-dimensional Broer-Kaup-Kupershmit equation | SHALLOW-WATER | VARIATIONAL METHOD | SOLITON-SOLUTIONS | PLASMA | HIGHER-ORDER | STABILITY ANALYSIS | Whitham-Broer-Kaup equation

Jacobi elliptic solutions | Drinfel'd–Sokolov–Wilson equation | (2+1)-dimensional Broer–Kaup–Kupershmit equation | Modified extended direct algebraic method | Whitham–Broer–Kaup equation | Traveling wave solutions | SYSTEM | PHYSICS, MULTIDISCIPLINARY | Drinfel'd-Sokolov-Wilson equation | ION-ACOUSTIC-WAVES | ZAKHAROV-KUZNETSOV EQUATION | NONLINEAR SCHRODINGER-EQUATION | (2+1)-dimensional Broer-Kaup-Kupershmit equation | SHALLOW-WATER | VARIATIONAL METHOD | SOLITON-SOLUTIONS | PLASMA | HIGHER-ORDER | STABILITY ANALYSIS | Whitham-Broer-Kaup equation

Journal Article

Pramana, ISSN 0304-4289, 9/2017, Volume 89, Issue 3, pp. 1 - 6

Nonlinear mathematical problems and their solutions attain much attention in solitary waves. In soliton theory, an efficient tool to attain various types of...

Astrophysics and Astroparticles | hbox {Exp}(-\varphi (\zeta ))$$ Exp ( - φ ( ζ ) ) -expansion technique | homogeneous principle | Drinfeld–Sokolov equation | Physics, general | exact and travelling wave solutions | Physics | Astronomy, Observations and Techniques | VARIATIONAL ITERATION METHOD | IMPROVED (G'/G)-EXPANSION METHOD | Drinfeld-Sokolov equation | PHYSICS, MULTIDISCIPLINARY | Exp(-phi(zeta))-expansion technique | EVOLUTION-EQUATIONS | Algorithms | Differential equations | Mathematical problems | Nonlinear equations | Solitary waves

Astrophysics and Astroparticles | hbox {Exp}(-\varphi (\zeta ))$$ Exp ( - φ ( ζ ) ) -expansion technique | homogeneous principle | Drinfeld–Sokolov equation | Physics, general | exact and travelling wave solutions | Physics | Astronomy, Observations and Techniques | VARIATIONAL ITERATION METHOD | IMPROVED (G'/G)-EXPANSION METHOD | Drinfeld-Sokolov equation | PHYSICS, MULTIDISCIPLINARY | Exp(-phi(zeta))-expansion technique | EVOLUTION-EQUATIONS | Algorithms | Differential equations | Mathematical problems | Nonlinear equations | Solitary waves

Journal Article

WSEAS Transactions on Mathematics, ISSN 1109-2769, 2017, Volume 16, pp. 276 - 282

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 02/2011, Volume 217, Issue 12, pp. 5743 - 5753

By using the (G′/G)-expansion method proposed recently, we give the exact travelling wave solutions of two different types of nonlinear evolution equations in...

(2+1) dimensional Boussinesq and Kadomtsev-Petviashvili equation | Travelling wave solutions | (G′/G)-expansion method | Integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota equation | (G '/G)-expansion method | LIE-ALGEBRAS | TRANSFORMATION | MATHEMATICS, APPLIED | HIERARCHY | Computation | Mathematical analysis | Nonlinear evolution equations | Traveling waves | Software | Mathematical models | Computer programs

(2+1) dimensional Boussinesq and Kadomtsev-Petviashvili equation | Travelling wave solutions | (G′/G)-expansion method | Integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota equation | (G '/G)-expansion method | LIE-ALGEBRAS | TRANSFORMATION | MATHEMATICS, APPLIED | HIERARCHY | Computation | Mathematical analysis | Nonlinear evolution equations | Traveling waves | Software | Mathematical models | Computer programs

Journal Article

Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 16, pp. 2867 - 2873

In this Letter, we consider a system of generalized Drinfeld–Sokolov (gDS) equations which models one-dimensional nonlinear wave processes in two-component...

Generalized Drinfeld–Sokolov equations | Tanh function method | Exact traveling wave solutions | Numerical solutions | Adomian's decomposition method | Generalized Drinfeld-Sokolov equations | exact traveling wave solutions | numerical solutions | PHYSICS, MULTIDISCIPLINARY | tanh function method | DECOMPOSITION METHOD | ALGORITHM | ADOMIAN POLYNOMIALS | KDV-BURGERS EQUATION | generalized Drinfeld-Sokolov equations | PARTIAL-DIFFERENTIAL-EQUATIONS | SOLITARY-WAVE SOLUTIONS | CONVERGENCE | NONLINEAR EVOLUTION-EQUATIONS | OPERATORS | TANH-FUNCTION METHOD

Generalized Drinfeld–Sokolov equations | Tanh function method | Exact traveling wave solutions | Numerical solutions | Adomian's decomposition method | Generalized Drinfeld-Sokolov equations | exact traveling wave solutions | numerical solutions | PHYSICS, MULTIDISCIPLINARY | tanh function method | DECOMPOSITION METHOD | ALGORITHM | ADOMIAN POLYNOMIALS | KDV-BURGERS EQUATION | generalized Drinfeld-Sokolov equations | PARTIAL-DIFFERENTIAL-EQUATIONS | SOLITARY-WAVE SOLUTIONS | CONVERGENCE | NONLINEAR EVOLUTION-EQUATIONS | OPERATORS | TANH-FUNCTION METHOD

Journal Article

Life Science Journal, ISSN 1097-8135, 07/2013, Volume 10, Issue 3, pp. 830 - 838

Journal Article

The European Physical Journal Plus, ISSN 2190-5444, 6/2015, Volume 130, Issue 6, pp. 1 - 17

We have derived the hierarchy of soliton equations associated with the untwisted affine Kac-Moody algebra D 4 (1) by calculating the corresponding recursion...

Condensed Matter Physics | Atomic, Molecular, Optical and Plasma Physics | Applied and Technical Physics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | KORTEWEG-DEVRIES EQUATION | REDUCTIONS | DRINFELD-SOKOLOV HIERARCHIES | DE VRIES EQUATION | WAVES | INVERSE SCATTERING | EVOLUTION | PHYSICS, MULTIDISCIPLINARY | KDV TYPE | INTEGRABLE HIERARCHIES | OPERATORS

Condensed Matter Physics | Atomic, Molecular, Optical and Plasma Physics | Applied and Technical Physics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | KORTEWEG-DEVRIES EQUATION | REDUCTIONS | DRINFELD-SOKOLOV HIERARCHIES | DE VRIES EQUATION | WAVES | INVERSE SCATTERING | EVOLUTION | PHYSICS, MULTIDISCIPLINARY | KDV TYPE | INTEGRABLE HIERARCHIES | OPERATORS

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2014, Volume 2014, Issue 1, pp. 1 - 11

In this paper we study the coupled Drinfeld-Sokolov-Satsuma-Hirota system, which was developed as one example of nonlinear equations possessing Lax pairs of a...

Ordinary Differential Equations | conservation laws | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | Lie symmetry methods | Jacobi elliptic function method | Partial Differential Equations | simplest equation method | coupled Drinfeld-Sokolov-Satsuma-Hirota system | EXPANSION METHOD | MATHEMATICS | MATHEMATICAL PHYSICS | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | PARTIAL-DIFFERENTIAL EQUATIONS | ELLIPTIC FUNCTION SOLUTIONS | Differential equations, Nonlinear | Mathematical research | Research | Conservation laws | Nonlinear equations | Boundary value problems | Hierarchies | Mathematical analysis | Exact solutions | Joining | Optimization | Symmetry

Ordinary Differential Equations | conservation laws | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | Lie symmetry methods | Jacobi elliptic function method | Partial Differential Equations | simplest equation method | coupled Drinfeld-Sokolov-Satsuma-Hirota system | EXPANSION METHOD | MATHEMATICS | MATHEMATICAL PHYSICS | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | PARTIAL-DIFFERENTIAL EQUATIONS | ELLIPTIC FUNCTION SOLUTIONS | Differential equations, Nonlinear | Mathematical research | Research | Conservation laws | Nonlinear equations | Boundary value problems | Hierarchies | Mathematical analysis | Exact solutions | Joining | Optimization | Symmetry

Journal Article

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