Solutions of Two- and Three-Dimensional Toda Lattice Equations in Terms of Various Forms of Bessel Functions

1985 ◽  
Vol 54 (10) ◽  
pp. 3701-3707 ◽  
Author(s):  
Noriko Saitoh ◽  
Shozo Takeno ◽  
Éi Iti Takizawa
Keyword(s):  
Bessel Functions ◽  
Toda Lattice ◽  
Three Dimensional ◽  
Toda Lattice Equations

scholarly journals Two-Dimensional Toda Lattice Equations

1988 ◽  
Vol 94 ◽  
pp. 42-58 ◽  
Author(s):  
Ryogo Hirota ◽  
Masaaki Ito ◽  
Fujio Kako
Keyword(s):  
Toda Lattice ◽  
Two Dimensional ◽  
Toda Lattice Equations

scholarly journals The modified Lax and two-dimensional Toda lattice equations associated with simple Lie algebras

1981 ◽  
Vol 1 (3) ◽  
pp. 361-380 ◽  
Author(s):  
George Wilson
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Toda Lattice ◽  
Evolution Equations ◽  
Gordon Equation ◽  
Two Dimensional ◽  
Simple Lie Algebras ◽  
Kdv Equations ◽  
Modified Kdv Equations ◽  
Toda Lattice Equations

AbstractWe associate to each complex simple Lie algebra g a hierarchy of evolution equations; in the simplest case g = sl(2) they are the modified KdV equations. These new equations are related to the two-dimensional Toda lattice equations associated with g in the same way that the modified KdV equations are related to the sinh-Gordon equation.

scholarly journals Exact solutions of asymmetric baroclinic quasi-geostrophic dipoles with distributed potential vorticity

2019 ◽  
Vol 868 ◽  
Author(s):  
A. Viúdez
Keyword(s):  
Exact Solution ◽  
Velocity Field ◽  
Potential Vorticity ◽  
Bessel Functions ◽  
Three Dimensional ◽  
Geophysical Flows ◽  
Radial Dependence ◽  
Vortex Dipole ◽  
Second Mode ◽  
Vorticity Anomaly

An exact solution of a baroclinic three-dimensional vortex dipole in geophysical flows with constant background rotation and constant background stratification is provided under the quasi-geostrophic (QG) approximation. The motion of the dipole is unsteady but the potential vorticity contours move rigidly. The vortex comprises three potential vorticity anomaly modes, with a radial dependence given by the spherical Bessel functions and with azimuthal and polar dependences given by the spherical harmonics. The first mode, or spherical mode, accounts for the horizontal asymmetry of the vortex dipole and curvature of the dipole’s horizontal trajectory. The second mode, or dipolar mode, accounts for the speed of displacement of the vortex dipole. A third mode, or vertical tilting mode, accounts for the dipole’s vertical asymmetry. The QG vertical velocity field has two contributions: the first one is octupolar and depends entirely on the dipolar mode, and the second one is dipolar and depends on the nonlinear interaction between dipolar and vertical tilting modes.

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