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The Benney equation in 1+1 dimensions is the nonlinear partial differential equation ...

The differential equation obtained by applying the biharmonic operator and setting to zero: del ^4phi=0. (1) In Cartesian coordinates, the biharmonic equation is del ^4phi = ...

The linear Boussinesq equation is the partial differential equation u_(tt)-alpha^2u_(xx)=beta^2u_(xxtt) (1) (Whitham 1974, p. 9; Zwillinger 1997, p. 129). The nonlinear ...

An Cesàro equation is a natural equation which expresses a curve in terms of its arc length function s(t) and radius of curvature rho(t) (or equivalently, the curvature ...

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general k×k matrix A, the ...

The octahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider an ...

A cubic equation is an equation involving a cubic polynomial, i.e., one of the form a_3x^3+a_2x^2+a_1x+a_0=0. Since a_3!=0 (or else the polynomial would be quadratic and not ...

The Diophantine equation x^2+y^2+z^2=3xyz. The Markov numbers m are the union of the solutions (x,y,z) to this equation and are related to Lagrange numbers.

Given a matrix equation Ax=b, the normal equation is that which minimizes the sum of the square differences between the left and right sides: A^(T)Ax=A^(T)b. It is called a ...

The partial differential equation u_(xy)+alphau_x+betau_y+gammau_xu_y=0.