scholarly journals Symmetry Analysis of an Interest Rate Derivatives PDE Model in Financial Mathematics

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1056 ◽  
Author(s):  
Bosiu C. Kaibe ◽  
John G. O’Hara
Keyword(s):  
Computer Software ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Financial Mathematics ◽  
Similarity Reduction ◽  
Interest Rate Derivatives ◽  
New Family ◽  
Point Transformations ◽  
Coupon Bond ◽  
Exact Invariant

We perform Lie symmetry analysis to a zero-coupon bond pricing equation whose price evolution is described in terms of a partial differential equation (PDE). As a result, using the computer software package SYM, run in conjunction with Mathematica, a new family of Lie symmetry group and generators of the aforementioned pricing equation are derived. We furthermore compute the exact invariant solutions which constitute the pricing models for the bond by making use of the derived infinitesimal generators and the associated similarity reduction equations. Using known solutions, we again compute more solutions via group point transformations.

scholarly journals Lie Symmetry Analysis for Soliton Solutions of Generalised Kadomtsev-Petviashvili-Boussinesq Equation in (3+1)-dimensions

2021 ◽  
Author(s):  
VISHAKHA JADAUN ◽  
Navnit Jha ◽  
Sachin Ramola
Keyword(s):  
Vector Fields ◽  
Evolution Equations ◽  
Invariant Solution ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Lie Symmetry ◽  
Similarity Reduction ◽  
Closed Form Solutions ◽  
Exact Invariant ◽  
Infinitesimal Transformations

The Lie group of infinitesimal transformations technique and similarity reduction is performed for obtaining an exact invariant solution to generalized Kadomstev-Petviashvili-Boussinesq (gKPB) equation in (3+1)-dimensions. We obtain generators of infinitesimal transformations, which provide us a set of Lie algebras. In addition, we get geometric vector fields, a commutator table of Lie algebra, and a group of symmetries. It is observed that the analytic solution (closed-form solutions) to the nonlinear gKPB evolution equations can easily be treated employing the Lie symmetry technique. A detailed geometrical framework related to the nature of the solutions possessing traveling wave, bright and dark soliton, standing wave with multiple breathers, and one-dimensional kink, for the appropriate values of the parameters involved.

Symmetry analysis with similarity reduction, new exact solitary wave solutions and conservation laws of (3 + 1)-dimensional extended quantum Zakharov–Kuznetsov equation in quantum physics

2021 ◽  
pp. 2150163
Author(s):  
Vinita ◽  
S. Saha Ray
Keyword(s):  
Conservation Laws ◽  
Quantum Physics ◽  
Physical Structure ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Similarity Reduction ◽  
Symmetry Approach ◽  
Simplest Equation Method ◽  
Lie Symmetry Approach ◽  
Conservation Theorem

A recently defined (3+1)-dimensional extended quantum Zakharov–Kuznetsov (QZK) equation is examined here by using the Lie symmetry approach. The Lie symmetry analysis has been used to obtain the varieties in invariant solutions of the extended Zakharov–Kuznetsov equation. Due to existence of arbitrary functions and constants, these solutions provide a rich physical structure. In this paper, the Lie point symmetries, geometric vector field, commutative table, symmetry groups of Lie algebra have been derived by using the Lie symmetry approach. The simplest equation method has been presented for obtaining the exact solution of some reduced transform equations. Finally, by invoking the new conservation theorem developed by Nail H. Ibragimov, the conservation laws of QZK equation have been derived.

Lie symmetry analysis, explicit solutions and conservation laws of the time fractional Clannish Random Walker’s Parabolic equation

2020 ◽  
pp. 2150074
Author(s):  
Panpan Wang ◽  
Wenrui Shan ◽  
Ying Wang ◽  
Qianqian Li
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Vector Fields ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Series Solutions ◽  
Lie Symmetry Analysis ◽  
Similarity Reduction ◽  
Power Series Solutions ◽  
Conservation Theorem

In this paper, we mainly study the symmetry analysis and conservation laws of the time fractional Clannish Random Walker’s Parabolic (CRWP) equation. The vector fields and similarity reduction of the time fractional CRWP equation are obtained. In addition, based on the power series theory, a simple and effective approach for constructing explicit power series solutions is proposed. Finally, by use of the new conservation theorem, the conservation laws of the time fractional CRWP equation are constructed.

Symmetry analysis and conservation laws of the time fractional Kaup-Kupershmidt equation from capillary gravity waves

2018 ◽  
Vol 13 (2) ◽  
pp. 24
Author(s):  
Zhonglong Zhao ◽  
Bo Han
Keyword(s):  
Conservation Laws ◽  
Gravity Waves ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Point Symmetries ◽  
Lie Symmetry Analysis ◽  
Similarity Reduction

The Lie symmetry analysis is employed to study the time fractional Kaup-Kupershmidt equation from capillary gravity waves. The Lie point symmetries and the similarity reduction of this equation are obtained. Then we construct the conservation laws by means of Ibragimov’s method.

Lie symmetry analysis and reduction for exact solution of (2+1)-dimensional Bogoyavlensky–Konopelchenko equation by geometric approach

2018 ◽  
Vol 32 (11) ◽  
pp. 1850127 ◽  
Author(s):  
S. Saha Ray
Keyword(s):  
Exact Solution ◽  
Differential Forms ◽  
Geometric Approach ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Invariance Group ◽  
Similarity Reduction ◽  
Lie Symmetry Method ◽  
Explicit Exact Solution ◽  
Symmetry Method

In this paper, the symmetry analysis and similarity reduction of the (2[Formula: see text]+[Formula: see text]1)-dimensional Bogoyavlensky–Konopelchenko (B–K) equation are investigated by means of the geometric approach of an invariance group, which is equivalent to the classical Lie symmetry method. Using the extended Harrison and Estabrook’s differential forms approach, the infinitesimal generators for (2[Formula: see text]+[Formula: see text]1)-dimensional B–K equation are obtained. Firstly, the vector field associated with the Lie group of transformation is derived. Then the symmetry reduction and the corresponding explicit exact solution of (2[Formula: see text]+[Formula: see text]1)-dimensional B–K equation is obtained.

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