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28 relations: Benjamin–Ono equation, Cauchy problem, Commutator, Continuum mechanics, Davey–Stewartson equation, Differential equation, Eigenvalues and eigenvectors, Function space, Hilbert space, Integrable system, Inverse scattering transform, Isospectral, Kadomtsev–Petviashvili equation, KdV hierarchy, Korteweg–de Vries equation, Lagrange, Euler, and Kovalevskaya tops, Mathematics, Nonlinear Schrödinger equation, Operator (mathematics), Peter Lax, Self-adjoint, Sine-Gordon equation, Skew-Hermitian matrix, Soliton, Spectrum (functional analysis), Sturm–Liouville theory, Toda lattice, Unitary operator.
Benjamin–Ono equation
In mathematics, the Benjamin–Ono equation is a nonlinear partial integro-differential equation that describes one-dimensional internal waves in deep water.
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Cauchy problem
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain.
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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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Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.
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Davey–Stewartson equation
In fluid dynamics, the Davey–Stewartson equation (DSE) was introduced in a paper by to describe the evolution of a three-dimensional wave-packet on water of finite depth.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Function space
In mathematics, a function space is a set of functions between two fixed sets.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Integrable system
In the context of differential equations to integrate an equation means to solve it from initial conditions.
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Inverse scattering transform
In mathematics, the inverse scattering transform is a method for solving some non-linear partial differential equations.
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Isospectral
In mathematics, two linear operators are called isospectral or cospectral if they have the same spectrum.
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Kadomtsev–Petviashvili equation
In mathematics and physics, the Kadomtsev–Petviashvili equation – or KP equation, named after Boris Borisovich Kadomtsev and Vladimir Iosifovich Petviashvili – is a partial differential equation to describe nonlinear wave motion.
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KdV hierarchy
In mathematics, the KdV hierarchy is an infinite sequence of partial differential equations which starts with the Korteweg–de Vries equation.
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Korteweg–de Vries equation
In mathematics, the Korteweg–de Vries equation (KdV equation for short) is a mathematical model of waves on shallow water surfaces.
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Lagrange, Euler, and Kovalevskaya tops
In classical mechanics, the precession of a rigid body such as a top under the influence of gravity is not, in general, an integrable problem.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Nonlinear Schrödinger equation
In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation.
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Operator (mathematics)
In mathematics, an operator is generally a mapping that acts on the elements of a space to produce other elements of the same space.
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Peter Lax
Peter David Lax (born 1 May 1926) is a Hungarian-born American mathematician working in the areas of pure and applied mathematics.
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Self-adjoint
In mathematics, an element x of a *-algebra is self-adjoint if x^*.
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Sine-Gordon equation
The sine-Gordon equation is a nonlinear hyperbolic partial differential equation in 1 + 1 dimensions involving the d'Alembert operator and the sine of the unknown function.
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Skew-Hermitian matrix
In linear algebra, a square matrix with complex entries is said to be skew-Hermitian or antihermitian if its conjugate transpose is equal to the original matrix, with all the entries being of opposite sign.
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Soliton
In mathematics and physics, a soliton is a self-reinforcing solitary wave packet that maintains its shape while it propagates at a constant velocity.
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Spectrum (functional analysis)
In mathematics, particularly in functional analysis, the spectrum of a bounded operator is a generalisation of the set of eigenvalues of a matrix.
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Sturm–Liouville theory
In mathematics and its applications, a classical Sturm–Liouville theory, named after Jacques Charles François Sturm (1803–1855) and Joseph Liouville (1809–1882), is the theory of a real second-order linear differential equation of the form where y is a function of the free variable x. Here the functions p(x), q(x), and w(x) > 0 are specified at the outset.
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Toda lattice
The Toda lattice, introduced by, is a simple model for a one-dimensional crystal in solid state physics.
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Unitary operator
In functional analysis, a branch of mathematics, a unitary operator is a surjective bounded operator on a Hilbert space preserving the inner product.
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References
[1] https://en.wikipedia.org/wiki/Lax_pair
