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Similarity solutions of dispersive long-wave equations in two space dimensions

✍ Scribed by Lou Sen-Yue

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
634 KB
Volume
18
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

In this paper, both the direct method and the non‐classical Lie approach are applied to reduce the (2 + 1)‐dimensional dispersive long wave equations. Nine types of two‐dimensional PDE reductions and 13 types of ODE reductions are given. All the known reductions obtained by the classical Lie approach are reobtained as some special cases. Similar to the (1 + 1)‐dimensional case, some types of reductions with essential and logarithmic singular characteristic manifolds are allowed although the model is integrable.

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Time Decay of Solutions for Generalized
Time Decay of Solutions for Generalized Boussinesq Equations in Two Space Dimensions
✍ Akmel Dé Godefroy 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 201 KB

In this article, we study the Cauchy problem of generalized Boussinesq equations. We prove the local existence in time in Sobolev and weighted Sobolev space through Fourier transforms. Then our main result is to prove that the supremum Ž . norm of the solution n, ¨with sufficiently small and regular