Absence of dissipative solutions of the schrodinger and klein-gordon equations with logarithmic
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1988
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Elsevier
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Abstract
It is shown that neither the Schrödinger equation nor the Klein-Gordon one with logarithmic nonlinearities have dissipative solutions. In the case of one-dimensional space, numerical experiments with different Cauchy data, in the nonrelativistic case, lead always to final states consisting only in oscillating gaussons.
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© Elsevier Science Publishers B.V. We are grateful to Professor A. Alvarez and Professor L. Vázquez for discussions. This work has been partially supported by Dirección General de Investigación Científica y Técnica, under grant PB86-0005.