Absense of dissipative solutions of the Schrödinger and Klein-Gordon equations with logarithmic nonlinearity
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1988
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Elsevier
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Abstract
It is shown that 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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© 1988 Published by Elsevier BV. We are grateful to Professor A. Alvarez and Professor L. Vazquez for discussions. This work has been partially supported by Dirección General de Investigación Científica y Técnica, under grant PB86-0005.