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The partial differential equation u_(xy)+(N(u_x+u_y))/(x+y)=0.

The partial differential equation (u_t)/(u_x)=1/4(u_(xxx))/(u_x)-3/8(u_(xx)^2)/(u_x^2)+3/2(p(u))/(u_x^2), where p(u)=1/4(4u^3-g_2u-g_3). The special cases ...

Differential Geometry

where R[nu]>-1, |argp|<pi/4, and a, b>0, J_nu(z) is a Bessel function of the first kind, and I_nu(z) is a modified Bessel function of the first kind.

The van der Pol equation is an ordinary differential equation that can be derived from the Rayleigh differential equation by differentiating and setting y=y^'. It is an ...

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 anti-self-dual Yang-Mills equation is the system of partial differential equations ...

The partial differential equation u_t+2uu_x-nuu_(xx)+muu_(xxx)=0.

The partial differential equation 3/4U_y+W_x=0, (1) where W_y+U_t-1/4U_(xxx)+3/2UU_x=0 (2) (Krichever and Novikov 1980; Novikov 1999). Zwillinger (1997, p. 131) and Calogero ...

The Hankel functions of the first kind are defined as H_n^((1))(z)=J_n(z)+iY_n(z), (1) where J_n(z) is a Bessel function of the first kind and Y_n(z) is a Bessel function of ...