Modulation Instability and Solitary Wave Analysis of the Ivancevic Option Pricing Model via Novel Mathematical Techniques

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan.

2 Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan.

3 Department of Mathematics and Information Technologies, Tashkent State Pedagogical University, Bunyodkor avenue, 27, Tashkent, 100070, Uzbekistan.

4 Civil and Environmental Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.

5 Operational Research Center in Healthcare, Near East University, Nicosia/TRNC, 99138 Mersin 10, Turkey.

Abstract

In academia, financial engineering challenges are very important, and there is an ongoing demand for effective
ways to examine and evaluate these models. The new extended direct algebraic approach and the new auxiliary
equation method have been used in this study to investigate the analytical solutions of the economically significant
model known as the Ivancevic option pricing model (IOPM) in the sense of new definition of M-truncated derivative.
Additionally, we will examine the equation’s modulation instability (MI) using linear stability approach
that demonstrates the accuracy and stability of all combined solutions. The analytical method of this model is
infrequently observed in the literature, despite the fact that numerous scholars have examined its applicability and
feasibility. The regulated Brownian motion associated with a non-linear Schr¨odinger type equation is described
by this model. Mathematical approaches are applied to generate the solution to understand the fluctuations in
market prices for the proposed model. The reaction of system to pulse propagation is explained through the use
of graphical representations in 2D, contour and 3D forms. Anticipating suitable parameter values that correspond
with the observed data is made possible by these illustrations. The sensitivity analysis predicts the model’s dependence
on the initial conditions. The findings of this study indicated that the suggested approaches preserved the
physical characteristics present in realistic processes while providing a very dependable and adaptable substitute
for problem-solving. Furthermore, we guarantee that all of the results demonstrate that these techniques are a
useful mathematical tool for identifying precise solitary wave solutions to nonlinear models that are present in
various scientific and technical domains.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 04 August 2025

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History

  • Receive Date: 04 May 2025
  • Revise Date: 10 July 2025
  • Accept Date: 28 July 2025

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