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Simple harmonic motion refers to the periodic sinusoidal oscillation of an object or quantity. Simple harmonic motion is executed by any quantity obeying the differential ...

The Ablowitz-Ramani-Segur conjecture states that a nonlinear partial differential equation is solvable by the inverse scattering method only if every nonlinear ordinary ...

Given a regular surface M, an asymptotic curve is formally defined as a curve x(t) on M such that the normal curvature is 0 in the direction x^'(t) for all t in the domain of ...

The partial differential equation u_t+u_x+uu_x-u_(xxt)=0 (Benjamin et al. 1972; Arvin and Goldstein 1985; Zwillinger 1997, p. 130). A generalized version is given by u_t-del ...

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

An ordinary differential equation of the form x^my^'=f(x,y), where m is a positive integer, f is analytic at x=y=0, f(0,0)=0, and f_y^'(0,0)!=0. Zwillinger (1997, p. 120), ...

The partial differential equation u_t+uu_x=nuu_(xx) (Benton and Platzman 1972; Zwillinger 1995, p. 417; Zwillinger 1997, p. 130). The so-called nonplanar Burgers equation is ...

This theorem states that, for a partial differential equation involving a time derivative of order n, the solution is uniquely determined if time derivatives up to order n-1 ...

The partial differential equation u_t+u_(xxxxx)+30uu_(xxx)+30u_xu_(xx)+180u^2u_x=0.

The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that describe the gravitational effects produced by a given mass ...