Non-existence and existence of localized solitary waves for the two-dimensional long-wave–short-wave interaction equations
✍ Scribed by H. Borluk; H.A. Erbay; S. Erbay
- Book ID
- 108052511
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 388 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0893-9659
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📜 SIMILAR VOLUMES
## Abstract We study the initial value problem where $ \|u(\cdot,t)\| = \int \nolimits ^ {\infty} \_ {- \infty}\varphi(x) | u( x,t ) | {\rm{ d }} x$ with φ(__x__)⩾0 and $ \int \nolimits^{\infty} \_ {-\infty} \varphi (x) \, {\rm{d}}x\,= 1$. We show that solutions exist globally for 0<__p__⩽1, while
## Abstract Let Ω be a domain in ℝ^__n__^ and let __m__ϵ ℕ; be given. We study the initial‐boundary value problem for the equation with a homogeneous Dirichlet boundary condition; here __u__ is a scalar function, \documentclass{article}\pagestyle{empty}\begin{document}$ \bar D\_x^m u: = (\partial \