Theta functions and non-linear equations 喜欢 0 阅读量: 165 作者: BA Dubrovin 摘要: CONTENTS Introduction Chapter I. Theta functions. General information § 1. Definition of theta functions and their simplest properties § 2. Theta functions of a single variable § 3. On Abelian tori § 4. ...
Theta functions and non-linear equations Theta functions of Riemann surfaces. The Jacobi inversion problem § 1. Periods of Abelian differentials on Riemann surfaces. Jacobi varieties § 2. Abel'... BA Dubrovin - 《Russ.math.surv》 被引量: 1056发表: 1981年 Tropical curves, their Jacobians ...
General methods for linear systems invoke the theta functions that are solutions of Fick's Second Law and equivalent Nernst-Planck equations, and approximations for non-linear problems. A compilation of transforms in the context of diffusion problems, and a series of examples are presented. ...
The second in a series of three volumes that survey the theory of theta functions, this volume emphasizes the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differentia...
x=ρcos(θ)sin(ϕ),y=ρsin(θ)sin(ϕ),andz=ρcos(ϕ),andρ2=x2+y2+z2.Also,dV=ρ2sin(ϕ)dρdϕdθ. ∭EzdV x2+y2+z2=1andx2+y2+z2=4 Triple Integrals Triple integrals using spherical coordinates ar...
Theta functions and non-linear equations CONTENTS Introduction Chapter I. Theta functions. General information § 1. Definition of theta functions and their simplest properties § 2. Theta functio... BA Dubrovin - 《Russ.math.surv》 被引量: 1055发表: 1981年 Action potentials and relations to the...
Learn more about this topic: Linear vs Nonlinear Functions | Differences & Examples from Chapter 3 / Lesson 3 280K Explore linear and nonlinear functions, understand what makes a function linear or nonlinear, and compare linear vs. nonlinear ...
Substituting in the 1-dimensional Jacobi functions θ3(τ)=∑m∈Zqm2 and θ2(τ)=∑m∈Zq(m+12)2 allows us to rewrite the equations. The functions Ad and Cd can then be represented as Ad(q)=θ3(Dτ)θ3(τ)+θ2(Dτ)θ2(τ), Cd(q)=θ3(Dτ)θ2(τ)+θ2(Dτ)θ3(τ)...
Lastly, future work should also focus on further characterization of the distinct functions and sources of slow and fast theta rhythms, with particular focus on examining how cholinergic modulation can elucidate the two-theta model at the cellular level. In summary, our findings provide evidence ...
Based on the Lenard recursion equations, we derive the Lax pair for the hierarchy of coupled long wave–short wave resonance equations, in which the first nontrivial member is the coupled long wave–short wave resonance equations. Resorting to the characteristic polynomial of Lax matrix for the ...