| 1. |
- Bennewitz, Christer
(författare)
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On the spectral problem associated with the Camassa-Holm equation
- 2004
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 11:4, s. 422-434
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Tidskriftsartikel (refereegranskat)abstract
- We give a basic uniqueness theorem in the inverse spectral theory for a Sturm-Liouville equation with a weight which is not of one sign. It is shown that the theorem may be applied to the spectral problem associated with the Camassa-Holm integrable system which models shallow water waves.
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| 2. |
- Byström, Johan
(författare)
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Correctors for some nonlinear monotone operators
- 2001
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 8:1, s. 8-30
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study homogenization of quasi-linear partial differential equations of the form -div (a (x, x/εh,Duh)) = fh on Ω with Dirichlet boundary conditions. Here the sequence (εh) tends to 0 as h→∞ and the map a (x, y, ξ) is periodic in y, monotone in ξ and satisfies suitable continuity conditions.W e prove that uh → u weakly in W1,p 0 (Ω) as h → ∞, where u is the solution of a homogenized problem of the form -div (b (x,Du)) = f on Ω. We also derive an explicit expression for the homogenized operator b and prove some corrector results, i.e. we find (Ph) such that Duh -Ph (Du) → 0 in Lp (Ω,Rn). () 0 in (Ω).
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| 3. |
- Constantin, Adrian, et al.
(författare)
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H-k metrics on the diffeomorphism group of the circle
- 2003
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 10:4, s. 424-430
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Tidskriftsartikel (refereegranskat)abstract
- Each H-k inner product, kis an element ofN, endows the diffeomorphism group of the circle with a Riemannian structure. For kgreater than or equal to1 the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of geodesics holds.
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| 4. |
- Constantin, Adrian, et al.
(författare)
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On the inverse scattering approach to the Camassa-Holm equation
- 2003
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 10:3, s. 252-255
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Tidskriftsartikel (refereegranskat)abstract
- A simple algoritm for the inverse scattering approach to the Camassa-Holm equation is presented.
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| 5. |
- Euler, Norbert, et al.
(författare)
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A tree of linearisable second-order evolution equations by generalised hodograph transformations
- 2001
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 8:3, s. 342-362
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Tidskriftsartikel (refereegranskat)abstract
- We present a list of (1 + 1)-dimensional second-order evolution equations all connected via a proposed generalised hodograph transformation, resulting in a tree of equations transformable to the linear second-order autonomous evolution equation. The list includes autonomous and nonautonomous equations
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| 6. |
- Euler, Norbert, et al.
(författare)
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Sundman symmetries of nonlinear second-order and third-order ordinary differential equations
- 2004
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 11:3, s. 399-421
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Tidskriftsartikel (refereegranskat)abstract
- Sundman symmetries arise from more general transformations than do point or contact symmetries. This paper first shows how to systematically calculate Sundman symmetries of second- and third-order nonlinear ordinary differential equations. Secondly, the authors illustrate the application of these symmetries by computing first integrals of the corresponding equations.
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| 7. |
- Gurjic, Z, et al.
(författare)
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The derivative nonlinear Schrodinger equation in analytic classes
- 2003
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 10:Suppl. 1, s. 62-71
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Tidskriftsartikel (refereegranskat)abstract
- The derivative nonlinear Schrodinger equation is shown to be locally well-posed in a class of functions analytic on a strip around the real axis. The main feature of the result is that the width of the strip does not shrink in time. To overcome the derivative loss, Kato-type smoothing results and space-time estimates are used.
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| 8. |
- Kalisch, Henrik
(författare)
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Periodic traveling water waves with isobaric streamlines
- 2004
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 11:4, s. 461-471
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that in water of finite depth, there are no periodic traveling waves with the property that the pressure in the underlying fluid flow is constant along streamlines. In the case of infinite depth, there is only one such solution, which is due to Gerstner.
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| 9. |
- Kurasov, Pavel, et al.
(författare)
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Essential spectrum due to singularity
- 2003
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 10, s. 93-106
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Tidskriftsartikel (refereegranskat)abstract
- It is proven that the essential spectrum of any self-adjoint operator associated with the matrix differential expression [GRAPHICS] consists of two branches. One of these branches (called regularity spectrum) can be obtained by approximating the operator by regular operators (with coefficients which are bounded near the origin), the second branch (called singularity spectrum) appears due to singularity of the coefficients.
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| 10. |
- Larsson, Daniel, et al.
(författare)
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Burchnall-Chaundy theory for q-difference operators and q-deformed Heisenberg algebras
- 2003
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Springer Science and Business Media LLC. - 1402-9251 .- 1776-0852. ; 10:Suppl. 2, s. 95-106
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to an extension of Burchnall-Chaundy theory on the interplay between algebraic geometry and commuting differential operators to the case of q-difference operators.
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