## Advances in Nonlinear Waves and Symbolic ComputationWith the rapid development of science and technology, the computer has become an important tool in many science fields. Particularly, symbolic computation, which is one of the most exciting and challenging areas. It has been applied in many sciences such as mathematics, physics, chemistry, biology, mechanics, engineering, etc., in particular, non-linear sciences ad complex sciences. Nowadays, many symbolic computation softwares have been used to deal with these problems. Up to now, there have existed many non-linear differential/difference systems related to solitons and chaos in the non-linear science field. In order to understand these complex physical phenomena, it is important to research some of their basic properties. Because of the complexity of these non-linear systems, with the symbolic computation, this new book presents important research on non-linear differential/difference systems, related to solitons and chaos as well as other non-linear sciences in views of constructive algorithms. |

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### Contents

Direct Methods and Symbolic Software for Conservation Laws | 19 |

Nonclassical Potential Symmetries for a Nonlinear Thermal Wave | 79 |

AntiDark Solitons of the Resonant Nonlinear Schrodinger | 99 |

Copyright | |

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### Common terms and phrases

Algorithm arbitrary associated ﬂux BLP equation Bluman candidate density chirped optical soliton chirped solitons completely integrable compression factor computation of conservation compute conservation laws conservation laws conserved densities constant DDEs densities and ﬂuxes density-ﬂux pairs dependent variables dilation invariance discrete doubly periodic solutions Euler operator evolution equations exact solutions example exponentially extended tanh method ﬁrst function further extended tanh Hereman higher order solitons homotopy operator inﬁnitely inﬁnitesimal KdV equation lattice laws of nonlinear Lett Lie group Liouville equations Maple Math modiﬁed monomials NLEEs NLSE non-travelling wave solutions nonclassical potential symmetries nonclassical symmetries nonlinear PDEs nonlinear wave obtain optical soliton package partial differential equations PDEs Phys physical polynomial potential system pulse compression satisﬁes scaling symmetry Section shiﬁs similarity solutions sine-Gordon equation solitary wave solitary wave solutions soliton pulse soliton solution solve symbolic computation symmetry reduction undetermined coefﬁcients undetermined coeﬂicients uniform in rank VCTanh wave equations