#### Title

Exact conditions for existence of homoclinic orbits in the fifth-order KdV model

#### Abbreviated Journal Title

Nonlinearity

#### Keywords

DIFFERENTIAL-EQUATIONS; WATER-WAVES; ORDERS; ASYMPTOTICS; SOLITONS; Mathematics, Applied; Physics, Mathematical

#### Abstract

We consider homoclinic orbits in the fourth-order equation v((iv)) + (1- epsilon(2)) v" - epsilon(2)v = v(2) + gamma(2vv" + v'(2)), where (gamma, epsilon) is an element of R-2. Numerical computations [CG97, C01] show that homoclinic orbits exist on certain curves gamma(epsilon) in the parameter plane (gamma, epsilon). We study the dependence. (gamma e) in the limit e -> 0 and prove that a curve gamma(epsilon) passes through the point (gamma(0), 0) only if s(gamma(0)) = 0, where s(gamma) denotes the Stokes constant for the truncated equation (with e = 0). The additional condition s'(gamma(0)) not equal 0 guarantees the existence of a unique curve. (e) passing through the point (gamma(0), 0). Every homoclinic orbit is proved to be single- humped for sufficiently small epsilon.

#### Journal Title

Nonlinearity

#### Volume

19

#### Issue/Number

10

#### Publication Date

1-1-2006

#### Document Type

Article

#### Language

English

#### First Page

2277

#### Last Page

2312

#### WOS Identifier

#### ISSN

0951-7715

#### Recommended Citation

"Exact conditions for existence of homoclinic orbits in the fifth-order KdV model" (2006). *Faculty Bibliography 2000s*. 6653.

http://stars.library.ucf.edu/facultybib2000/6653

## Comments

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