Novikov–Veselov equation

In mathematics, the Novikov–Veselov equation (or Veselov–Novikov equation) is a natural (2+1)-dimensional analogue of the Korteweg–de Vries (KdV) equation. ^[1]

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Table of Contents

1. 22 relations: Clifford S. Gardner, Commutator, Complex analysis, Complex number, Holomorphic function, Integrable system, Inverse scattering transform, John M. Greene, Kadomtsev–Petviashvili equation, Korteweg–De Vries equation, Lax pair, Martin David Kruskal, Mathematics, Nonlinear Schrödinger equation, Partial differential equation, Peter Lax, Robert M. Miura, Schrödinger equation, Sergei Novikov (mathematician), Sine-Gordon equation, Soliton, Vladimir E. Zakharov.

2. Integrable systems
3. Solitons

Clifford S. Gardner

Clifford Spear Gardner (January 14, 1924 – September 25, 2013) was an American mathematician specializing in applied mathematics.

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Commutator

In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.

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Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

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Complex number

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^.

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Holomorphic function

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space.

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Integrable system

In mathematics, integrability is a property of certain dynamical systems. Novikov–Veselov equation and Integrable system are integrable systems and partial differential equations.

See Novikov–Veselov equation and Integrable system

Inverse scattering transform

In mathematics, the inverse scattering transform is a method that solves the initial value problem for a nonlinear partial differential equation using mathematical methods related to wave scattering. Novikov–Veselov equation and inverse scattering transform are Exactly solvable models, integrable systems and partial differential equations.

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John M. Greene

John Morgan Greene (22 September 1928 – 22 October 2007) was an American theoretical physicist and applied mathematician, known for his work on solitons and plasma physics.

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Kadomtsev–Petviashvili equation

In mathematics and physics, the Kadomtsev–Petviashvili equation (often abbreviated as KP equation) is a partial differential equation to describe nonlinear wave motion. Novikov–Veselov equation and Kadomtsev–Petviashvili equation are Exactly solvable models, integrable systems, partial differential equations and solitons.

See Novikov–Veselov equation and Kadomtsev–Petviashvili equation

Korteweg–De Vries equation

In mathematics, the Korteweg–De Vries (KdV) equation is a partial differential equation (PDE) which serves as a mathematical model of waves on shallow water surfaces. Novikov–Veselov equation and Korteweg–De Vries equation are Exactly solvable models, integrable systems, partial differential equations and solitons.

See Novikov–Veselov equation and Korteweg–De Vries equation

Lax pair

In mathematics, in the theory of integrable systems, a Lax pair is a pair of time-dependent matrices or operators that satisfy a corresponding differential equation, called the Lax equation. Novikov–Veselov equation and Lax pair are Exactly solvable models.

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Martin David Kruskal

Martin David Kruskal (September 28, 1925 – December 26, 2006) was an American mathematician and physicist.

See Novikov–Veselov equation and Martin David Kruskal

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Novikov–Veselov equation and Mathematics

Nonlinear Schrödinger equation

In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. Novikov–Veselov equation and nonlinear Schrödinger equation are Exactly solvable models, integrable systems and partial differential equations.

See Novikov–Veselov equation and Nonlinear Schrödinger equation

Partial differential equation

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. Novikov–Veselov equation and partial differential equation are partial differential equations.

See Novikov–Veselov equation and Partial differential equation

Peter Lax

Peter David Lax (born Lax Péter Dávid; 1 May 1926) is a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics.

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Robert M. Miura

Robert M. Miura (September 12, 1938 - November 25, 2018) was a Distinguished Professor of Mathematical Sciences and of Biomedical Engineering at New Jersey Institute of Technology (NJIT) in Newark, New Jersey.

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Schrödinger equation

The Schrödinger equation is a partial differential equation that governs the wave function of a quantum-mechanical system. Novikov–Veselov equation and Schrödinger equation are partial differential equations.

See Novikov–Veselov equation and Schrödinger equation

Sergei Novikov (mathematician)

Sergei Petrovich Novikov (Russian: Серге́й Петро́вич Но́виков; 20 March 19386 June 2024) was a Soviet and Russian mathematician, noted for work in both algebraic topology and soliton theory.

See Novikov–Veselov equation and Sergei Novikov (mathematician)

Sine-Gordon equation

The sine-Gordon equation is a second-order nonlinear partial differential equation for a function \varphi dependent on two variables typically denoted x and t, involving the wave operator and the sine of \varphi. Novikov–Veselov equation and sine-Gordon equation are Exactly solvable models and solitons.

See Novikov–Veselov equation and Sine-Gordon equation

Soliton

In mathematics and physics, a soliton is a nonlinear, self-reinforcing, localized wave packet that is strongly stable, in that it preserves its shape while propagating freely, at constant velocity, and recovers it even after collisions with other such localized wave packets. Novikov–Veselov equation and soliton are integrable systems, partial differential equations and solitons.

See Novikov–Veselov equation and Soliton

Vladimir E. Zakharov

Vladimir Evgen'evich Zakharov (Влади́мир Евге́ньевич Заха́ров; 1 August 1939 – 20 August 2023) was a Soviet and Russian mathematician and physicist.

See Novikov–Veselov equation and Vladimir E. Zakharov

See also

Integrable systems

• AKNS system
• Bäcklund transform
• Benjamin–Ono equation
• Bullough–Dodd model
• Calogero–Degasperis–Fokas equation
• Camassa–Holm equation
• DBAR problem
• Davey–Stewartson equation
• Dispersionless equation
• Drinfeld–Sokolov–Wilson equation
• Dym equation
• Ernst equation
• Four-dimensional Chern–Simons theory
• Frobenius manifold
• Gardner equation
• Gelfand–Zeitlin integrable system
• Hitchin system
• Integrable algorithm
• Integrable system
• Inverse scattering transform
• Ishimori equation
• Kadomtsev–Petviashvili equation
• Kaup–Kupershmidt equation
• Korteweg–De Vries equation
• Liouville–Arnold theorem
• List of integrable models
• Modified Korteweg-De Vries equation
• Nahm equations
• Nonlinear Schrödinger equation
• Novikov–Veselov equation
• ODE/IM correspondence
• Riemann–Hilbert problem
• Six-dimensional holomorphic Chern–Simons theory
• Soliton
• Superintegrable Hamiltonian system
• Tau function (integrable systems)
• Toda field theory
• Toda lattice
• Volterra lattice
• W-algebra
• Ward's conjecture

Solitons

• Bäcklund transform
• Bogomol'nyi–Prasad–Sommerfield bound
• Camassa–Holm equation
• Compacton
• Degasperis–Procesi equation
• Derrick's theorem
• Dissipative soliton
• Domain wall
• Domain wall (string theory)
• Dym equation
• Frenkel–Kontorova model
• Hunter–Saxton equation
• Kadomtsev–Petviashvili equation
• KdV hierarchy
• Korteweg–De Vries equation
• Linear stability
• Loop group
• Lugiato–Lefever equation
• Nematicon
• Non-topological soliton
• Nonlinear partial differential equation
• Novikov–Veselov equation
• Orbital stability
• Oscillon
• Peakon
• Peregrine soliton
• Q-ball
• Riemann–Hilbert problem
• Robin Bullough
• Sine-Gordon equation
• Soliton
• Soliton (optics)
• Tau function (integrable systems)
• Toda lattice
• Topological defect
• Topological quantum number
• Vakhitov–Kolokolov stability criterion

References

[1] https://en.wikipedia.org/wiki/Novikov–Veselov_equation

Also known as Veselov-Novikov equation.

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