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      On the construction of conservation laws: a mixed approach

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          Abstract

          A new approach, combining the Ibragimov method and the one by Anco and Bluman, with the aim of algorithmically computing local conservation laws of partial differential equations, is discussed. Some examples of the application of the procedure are given. The method, of course, is able to recover all the conservation laws found by using the direct method; at the same time we can characterize which symmetry, if any, is responsible for the existence of a given conservation law. Some new local conservation laws for the Short Pulse equation and for the Fornberg Whitham equation are also determined.

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          A new conservation theorem

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            Propagation of ultra-short optical pulses in cubic nonlinear media

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              The short pulse equation is integrable

              We prove that the Schafer-Wayne short pulse equation (SPE) which describes the propagation of ultra-short optical pulses in nonlinear media is integrable. First, we discover a Lax pair of the SPE which turns out to be of the Wadati-Konno-Ichikawa type. Second, we construct a chain of transformations which relates the SPE with the sine-Gordon equation.
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                Author and article information

                Journal
                2016-12-14
                Article
                1612.04859

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                Submitted for publication on Journal of Mathematical physics (16/05/2016)
                math-ph math.MP

                Mathematical physics, Mathematical & Computational physics

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