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Event SMS Weekly Talk
Date 10/10/2019
Time 14:00
Venue ASSMS Main Hall
Title CLASSIFICATION OF INVARIANT SOLUTIONS FOR A NON-LINEAR WAVE EQUATION
Speaker Ali Raza Bhatti
Abstract

MY AIM IN THIS TALK IS TO DIVIDE THE SET OF ALL INVARIANT
SOLUTIONS OF A GIVEN DIFFERENTIAL EQUATION INTO
EQUIVALENCE CLASSES. TWO INVARIANT SOLUTIONS ARE
EQUIVALENT IF ONE CAN BE MAPPED TO THE OTHER BY A POINT
SYMMETRY OF THE DIFFERENTIAL EQUATION. CLASSIFICATION
GREATLY SIMPLIFIES THE PROBLEM OF DETERMINING ALL
INVARIANT SOLUTIONS. IT IS ONLY NECESSARY TO FIND ONE
GENERAL INVARIANT SOLUTION FROM EACH CLASS; THEN THE
WHOLE CLASS CAN BE CONSTRUCTED BY APPLYING THE
SYMMETRIES. THIS STRATEGY MINIMIZES THE EFFORT NEEDED

TO OBTAIN INVARIANT SOLUTIONS. WE DISCUSS THE ONE-
DIMENSIONAL OPTIMAL SYSTEM OF SUB-ALGEBRAS FOR A WAVE

EQUATION WITH ARBITRARY FUNCTION. IN PARTICULAR, I WILL
START WITH THE PRINCIPAL LIE ALGEBRA AND CONSTRUCT A

SET OF SYMMETRY TRANSFORMATIONS THAT FORM A ONE-
DIMENSIONAL OPTIMAL SYSTEM FOR THE GIVEN EQUATION.

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