Solutions to the nonlinear Schrodinger equation carrying by Mahmoudi F., Malchiodi A., Montenegro M.

By Mahmoudi F., Malchiodi A., Montenegro M.

Show description

Read or Download Solutions to the nonlinear Schrodinger equation carrying momentum along a curve. I study of the limit set and approximate solutions PDF

Similar mathematics books

Mathematics of Complexity and Dynamical Systems

Arithmetic of Complexity and Dynamical platforms is an authoritative connection with the fundamental instruments and ideas of complexity, structures concept, and dynamical platforms from the point of view of natural and utilized arithmetic.   advanced platforms are platforms that include many interacting elements being able to generate a brand new caliber of collective habit via self-organization, e.

GRE Math Prep Course

Each year scholars pay up to $1000 to check prep businesses to organize for the GMAT. you can now get an identical coaching in a publication. GMAT Prep direction offers the similar of a two-month, 50-hour direction. even though the GMAT is a tricky attempt, it's a very learnable attempt. GMAT Prep direction offers an intensive research of the GMAT and introduces a variety of analytic thoughts that can assist you immensely, not just at the GMAT yet in company university besides.

Optimization and Control with Applications

This ebook includes refereed papers that have been offered on the thirty fourth Workshop of the foreign tuition of arithmetic "G. Stampacchia,” the overseas Workshop on Optimization and keep an eye on with purposes. The e-book includes 28 papers which are grouped in accordance with 4 extensive subject matters: duality and optimality stipulations, optimization algorithms, optimum keep watch over, and variational inequality and equilibrium difficulties.

Spaces of neoliberalization: towards a theory of uneven geographical development

In those essays, David Harvey searches for sufficient conceptualizations of house and of asymmetric geographical improvement that might support to appreciate the hot ancient geography of world capitalism. the speculation of asymmetric geographical improvement wishes extra exam: the intense volatility in modern political fiscal fortunes throughout and among areas of the realm economic climate cries out for higher historical-geographical research and theoretical interpretation.

Additional info for Solutions to the nonlinear Schrodinger equation carrying momentum along a curve. I study of the limit set and approximate solutions

Sample text

Rn−1 Rn−1 U (kz)p−2 ∂m U (kz)wr2 = 1 hk wr ∂m F. Rn−1 Hence A4 can be written as A4 = − + 1 k 2 H l ∂ml U (kz) + (f )2 ∂m U (kz) wr k Rn−1 l H l (zl + Φl ) l 2 wr − (f ) U (kz)H m N − k∂m U (kz) ∇ V, z + Φ − hU (kz) ∇N V, Em Rn−1 ∂m U (kz) wr ∇N V, z + Φ + 2(f )2 H, z + Φ wr + Rn−1 + h2 k 2 H l ∂l wr . ∂m U (kz) Rn−1 l 32 After some cancelations and some integration by parts we find the following formula Hl A4 = −2k Rn−1 l 2 wr ∂ml U (kz) + p−1 2 k 2kθ wr U (kz). Rn−1 Using the symmetries of the integrals we find 1 n−1 = −2kH m A4 = −2kH m p−1 wr U (kz) 2θ Rn−1 1 p−1 1 + − U p (kz) .

5. 37 Proof of (35). 5, taking into account (19) and (20) we obtain (66) Σ1 + Σ2 = 0, where Σ1 A2 σhσ−1 = γ ∂h N ∇ V, V ds + ∂V Aσ(σ − 1)hσ−2 γ ∂h N ∂h ∂h N ∇ V, W + A ∇ V, V ds ∂V ∂A 2 ∂V ∂2h ∂2h N ∇ V, W + + Aσhσ−1 A ∇N V, V ds + ∂V 2 ∂V ∂A 2 γ ∂h N − A2 hσ H, V ds − Aσhσ−1 ∇ V, V H, W ds ∂V γ γ − ∂h ∂h N ∇ V, W + A ∂V ∂A 2 hσ−1 Aσ γ  ˙j− V˙ j W Ahσ  = γ R1j1m V j W m  ds + A1 A2 σ j γ ∂h ds + AA1 σ(σ − 1) ∂A 2 γ 2 ∂h N ∂h ∇ V, W + A ds − A1 ∂V ∂A 2 hσ−1 γ ∂h ds ∂A ∂h N ∂h ∂h ∇ V, W + A2 ds ∂V ∂A ∂A hσ−2 ∂ h ∂ h ∇N V, W + A ds − AA1 σ ∂A∂V ∂A2 2 hσ−1 γ + A1 σ hσ−1 γ j,m hσ−1 + AA12 σ + AA1 σ γ ∂h (∇N )2 V [V, W]ds ∂V H, V ds;  Σ2 Aσhσ−1 hσ−1 γ ∂h H, W ds ∂A hσ H, W ds + A12 γ hσ ds.

54 (2005), no. 2, 443-464. [34] Kwong, M. , Uniqueness of positive solutions of −∆u + u + up = 0 in Rn , Arch. Rational Mech. Anal. 105, (1989), 243-266. [35] Li, Y. , On a singularly perturbed equation with Neumann boundary conditions, Comm. Partial Differential Equations 23 (1998), 487-545. , The Dirichlet problem for singularly perturbed elliptic equations, Comm. Pure Appl. Math. 51 (1998), 1445-1490. , Large amplitude stationary solutions to a chemotaxis systems, J. Differential Equations, 72 (1988), 1-27.

Download PDF sample

Rated 4.03 of 5 – based on 45 votes