*Extreme wave events, also referred to as*

freak or rogue waves, are mostly known as an oceanic

phenomenon responsible for a large number of maritime

disasters. These waves, which have height and steepness

much greater than expected from the sea average

state [1], have recently become a topic of intense research.

Freak waves appear both in deep ocean and in shallow

waters [2]. In contrast to tsunamis and storms associated

with typhoons that can be predicted hours (sometimes

days) in advance, the particular danger of oceanic rogue

waves is that they suddenly appear from nowhere only

seconds before they hit a ship. The grim reality, however,

is that although the existence of freak waves has now been

confirmed by multiple observations, uncertainty remains

on their fundamental origins. This hinders systematic

approaches to study their characteristics, including the

predictability of their appearance [3].

In fact, research on rogue waves is in an emerging state

[1, 3, 4]. These waves not only appear in oceans [5] but

also in the atmosphere [7], in optics [8, 9], in plasmas

[11], in superfluids, in Bose-Einstein condensates [12] and

also as capillary waves [13]. The common features and

differences among freak wave manifestations in their different

contexts is a subject of intense discussion [2]. New

studies of rogue waves in any of these disciplines enrich

their concept and lead to progress towards a comprehensive

understanding of a phenomenon which still remains

largely unexplored. A formal mathematical description

of a rogue wave is provided by the so-called Peregrine

soliton [14]. This solitary wave is a solution of the one-dimensional

nonlinear Schr¨odinger equation (NLSE) with

the property of being localized in both the transverse and

the longitudinal coordinate: thus it describes a unique

wave event. This solution is also unique in a mathematical

sense, as it is written in terms of rational functions

of coordinates, in contrast to most of other known solutions

of the NLSE.

In a variety of complex systems such as Bose–Einstein

condensates [22], optical fibers [23], and financial systems

[24, 25], several variables rather than a single wave

amplitude need to be considered. For instance, in the financial

world it is necessary to couple cash to the value of

other assets such as shares, bonds, options, etc., as well

as to consider all correlations between these variables.

The resulting systems of equations may thus describe extreme

waves with higher accuracy than the single NLSE

model. Approaches to rogue wave phenomena involving

multiple coupled waves are the coupled Gross-Pitaevskii

(GP) equations [26] and the Manakov system (or vector

NLSE) [27]. Indeed, vector rogue waves of GP equations

and the Manakov system have been recently presented

[22, 25, 28].

Conclusions. Here we have analytically constructed

and discussed, a multi-parametric vector freak solution

of the vector NLSE. This family of exact solutions includes

known vector Peregrine (rational) solutions, and

novel freak solutions which feature both exponential and

rational dependence on coordinates. Because of the universality

of the vector NLSE model (1), our solutions

contribute to a better control and understanding of rogue

wave phenomena in a variety of complex dynamics, ranging

from optical communications to Bose-Einstein condensates

and financial systems

freak or rogue waves, are mostly known as an oceanic

phenomenon responsible for a large number of maritime

disasters. These waves, which have height and steepness

much greater than expected from the sea average

state [1], have recently become a topic of intense research.

Freak waves appear both in deep ocean and in shallow

waters [2]. In contrast to tsunamis and storms associated

with typhoons that can be predicted hours (sometimes

days) in advance, the particular danger of oceanic rogue

waves is that they suddenly appear from nowhere only

seconds before they hit a ship. The grim reality, however,

is that although the existence of freak waves has now been

confirmed by multiple observations, uncertainty remains

on their fundamental origins. This hinders systematic

approaches to study their characteristics, including the

predictability of their appearance [3].

In fact, research on rogue waves is in an emerging state

[1, 3, 4]. These waves not only appear in oceans [5] but

also in the atmosphere [7], in optics [8, 9], in plasmas

[11], in superfluids, in Bose-Einstein condensates [12] and

also as capillary waves [13]. The common features and

differences among freak wave manifestations in their different

contexts is a subject of intense discussion [2]. New

studies of rogue waves in any of these disciplines enrich

their concept and lead to progress towards a comprehensive

understanding of a phenomenon which still remains

largely unexplored. A formal mathematical description

of a rogue wave is provided by the so-called Peregrine

soliton [14]. This solitary wave is a solution of the one-dimensional

nonlinear Schr¨odinger equation (NLSE) with

the property of being localized in both the transverse and

the longitudinal coordinate: thus it describes a unique

wave event. This solution is also unique in a mathematical

sense, as it is written in terms of rational functions

of coordinates, in contrast to most of other known solutions

of the NLSE.

In a variety of complex systems such as Bose–Einstein

condensates [22], optical fibers [23], and financial systems

[24, 25], several variables rather than a single wave

amplitude need to be considered. For instance, in the financial

world it is necessary to couple cash to the value of

other assets such as shares, bonds, options, etc., as well

as to consider all correlations between these variables.

The resulting systems of equations may thus describe extreme

waves with higher accuracy than the single NLSE

model. Approaches to rogue wave phenomena involving

multiple coupled waves are the coupled Gross-Pitaevskii

(GP) equations [26] and the Manakov system (or vector

NLSE) [27]. Indeed, vector rogue waves of GP equations

and the Manakov system have been recently presented

[22, 25, 28].

Conclusions. Here we have analytically constructed

and discussed, a multi-parametric vector freak solution

of the vector NLSE. This family of exact solutions includes

known vector Peregrine (rational) solutions, and

novel freak solutions which feature both exponential and

rational dependence on coordinates. Because of the universality

of the vector NLSE model (1), our solutions

contribute to a better control and understanding of rogue

wave phenomena in a variety of complex dynamics, ranging

from optical communications to Bose-Einstein condensates

and financial systems

Begin forwarded message:

From: nick herbert <

Subject: deterministic vector freak waves

Date: April 15, 2012 3:07:37 AM GMT+01:00

==========================================

deterministic vector freak waves

http://xxx.lanl.gov/abs/1204.1449

==========================================

I think you should make it clear, David,

that this paper has absolutely nothing to do with

"The Hippies That Saved Physics"