Multidimensional Laplace transforms for solution of nonlinear equations

PRANC: Program for Analyzing Nonlinear Circuits.

“…*A n ~ v t. = t The general forms in eqns. (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12), (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) and will be used in sections (2-3) and (2)(3)(4). The salient feature in each of these equations is how an nth degree polynomiaL function in the time-domain is represented by the nth-order product of the transform of the function in the transform domain.…”

Volterra analysis of the Non-linear Magneto-Optic Recording Channel

“…Presently, it is pervading High Energy Physics particle detectors, wideband amplifiers, satellite communications [1] and other areas of science and technology. To cite some of the areas of interest, it occurs in many types of devices such as Mechanical [2], Acoustical (Microphones for instance), Electronic [3] and Microelectronic [4], Microwave [5], Optical [6], Magnetic [7] and Superconducting [8]. Parasitic frequency terms appear either at integer multiple of the base frequency (harmonic) or as a mixture of two or several multiples of base frequencies (intermodulation) when several base frequencies are used (as in modulation systems for instance).…”

Associated transforms for solution of nonlinear equations

“…Its n-dimensional inverse can be found by the integral f(tl,t2,...,t,) =_ L' [F(s,s2,...,sn);tl,t2,... ,t,] In certain nonlinear systems analysis, particularly in Volterra series applications [1][2] on Nonlinear systems [3][4][5], it becomes necessary to take the inverse of the n-dimensional Laplace transform and specify this inverse image in the special case: t t2 tn t. We denote this image function of one variable by g(t), or g(t) f(t,tz,...,tn)],,=,, ,.=, (1.2) An alternative approach to obtain the time function, g(t), is to associate with given F(s,s,...,sn) a function G(s) from which a direct application of the one-dimensional inverse transform yields g(t). This special method of computing the inverse transform is said to be the association of variables.…”