Abstract
Let us consider the Fourier transform method for solving the linear partial differential equation. It is known that the Fourier transformation converts this equation into a linear ordinary differential equation, which can be easily integrated. Thus we obtain the evolution of Fourier components of the initial data in the problem under consideration. Inverse Fourier transformation yields the solution of initial equation in the integral form. It would be more correct to say that the Fourier transforms method permits to solve the Cauchy problem of a linear partial differential equation. This is the main reason why this method is attractive to apply in mathematical physics.
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© 1999 Springer Science+Business Media Dordrecht
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Maimistov, A.I., Basharov, A.M. (1999). Inverse Scattering Transform Method. In: Nonlinear Optical Waves. Fundamental Theories of Physics, vol 104. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2448-7_3
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DOI: https://doi.org/10.1007/978-94-017-2448-7_3
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