DataVXAIP AdvancesPaper
journal article·2023-12-01Open access

Exact and solitary wave structure of the tumor cell proliferation with LQ model of three dimensional PDE by newly extended direct algebraic method

Sidra Ghazanfar, Nauman Ahmed, Syed Mansoor Ali, Muhammad Sajid Iqbal, Ali Akgül, Muhammad Ali Shar, Abdul Bariq

AIP Advances· Volume 13· Issue 12
Publisher pageOpen full text
Source abstract

Abstract

An essential stage in the spread of cancer is the entry of malignant cells into the bloodstream. The fundamental mechanism of cancer cell intravasation is still completely unclear, despite substantial advancements in observing tumor cell mobility in vivo. By creating therapeutic methods in conjunction with control engineering or by using the models for simulations and treatment process evaluation, tumor growth models have established themselves as a crucial instrument for producing an engineering backdrop for cancer therapy. Because tumor growth is a highly complex process, mathematical modeling has been essential for describing it because a carefully crafted tumor growth model constantly describes the measurements and the physiological processes of the tumors. This article discusses the exact and solitary wave behavior of a tumor cell with a three-dimensional linear-quadratic model. Exact solutions have been discussed in detail using the newly extended direct algebraic method, which presents a variety of answers to this issue based on the conditions applied. This article also illustrates its graphical behavior with surface and contour plots of several solitons.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Mathematical Biology Tumor Growth · Differential Equations and Numerical Methods · Microtubule and mitosis dynamics

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Mathematics and Statistics, The University of Lahore 1 , Lahore, Pakistan

Department of Computer Science and Mathematics, Lebanese American University 2 , Beirut, Lebanon

Department of Mathematics 3 , Mathematics Research Center, Near East University, Near East Boulevard, PC: 99138 Nicosia /Mersin 10, Türkiye

Department of Physics and Astronomy, College of Science, King Saud University 4 , P.O. BOX 2455, Riyadh 11451, Saudi Arabia

5 School of Foundation Studies and Mathematics, OUC with Liverpool john Moores University (UK), Qatar Campus, 12253 Doha, Qatar

6 Department of Humanities & Basic Science, Military College of Signals, NUST, Islamabad, Pakistan.

7 IRO, Research Center, University of Halabja, Halabja, 46018, Iraq

Department of Mathematics 8 , Art and Science Faculty, Siirt University, TR-56100 Siirt, Türkiye

Department of Mechanical and Energy Systems Engineering, Faculty of Engineering and Informatics, University of Bradford 9 , Bradford BD7 1DP, United Kingdom

Department of Mathematics, Laghman University 10 , Mehtarlam City, 2701 Laghman, Afghanistan

References (25)

Show source-provided references
1. Do the shocks in technological and financial innovation influence the environmental quality? Evidence from brics economies10.1016/j.techsoc.2021.101828 ↗
2. Quan-Hoang · 2023
3. Jakobsen · 2022 · 1
4. Fifth-order comprehensive adjoint sensitivity analysis methodology for nonlinear systems (5th-CASAM-N): II. Paradigm application to a Bernoulli model comprising uncertain parameters10.4236/ajcm.2022.121008 ↗
5. Exact travelling wave solutions of the nonlinear evolution equations by improved f-expansion in mathematical physics10.33434/cams.659225 ↗
6. On the examination of optical soliton pulses of Manakov system with auxiliary equation technique10.1016/j.ijleo.2022.169800 ↗
7. Optical solitons and other solutions to Biswas–Arshed equation using the extended simplest equation method10.1016/j.ijleo.2019.03.112 ↗
8. Topological solitons of resonant nonlinear Schödinger’s equation with dual-power law nonlinearity by G′/G-expansion technique10.1016/j.ijleo.2014.03.042 ↗
9. The Riccati–Bernoulli sub-ode technique for solving the deterministic (stochastic) generalized-Zakharov system10.24294/ijmss.v1i3.810 ↗
10. Imaging ultrasound propagation using the Westervelt equation by the generalized Kudryashov and modified Kudryashov methods10.3390/app122211813 ↗
11. Existence and regularity of shock-effected solitons for nonlinear problems in electro-cardiac-physiology10.1142/s0219691322500539 ↗
12. Novel explicit solutions for the nonlinear Zoomeron equation by using newly extended direct algebraic technique10.1007/s11082-019-2162-8 ↗
13. Weakly nonlinear electron-acoustic waves in the fluid ions propagated via a (3 + 1)-dimensional generalized Korteweg–de-Vries–Zakharov–Kuznetsov equation in plasma physics10.1016/j.rinp.2021.105069 ↗
14. Diverse acoustic wave propagation to confirmable time–space fractional KP equation arising in dusty plasma10.1088/1572-9494/ac18bb ↗
15. Investigation the soliton solutions of Mussel and Algae model leading to concentration10.1016/j.aej.2023.01.025 ↗
16. Selection of solitons coinciding the numerical solutions for uniquely solvable physical problems: A comparative study for the nonlinear stochastic Gross–Pitaevskii equation in dispersive media10.1142/s0217979223501916 ↗
17. Comparative analysis of numerical with optical soliton solutions of stochastic Gross–Pitaevskii equation in dispersive media10.1016/j.rinp.2022.106175 ↗
18. Nonlinear solitary waves in particle metamaterials with local resonators10.1121/10.0009631 ↗
19. Ionization theory and radio-biological reactions10.1073/pnas.23.4.189 ↗
20. Mathematical modeling of tumor growth and treatment10.2174/1381612819666131125150434 ↗
21. Mathematical model of tumor–immune surveillance10.1016/j.jtbi.2016.06.012 ↗
22. Premalignant tumors and conditions of bone10.1097/00000478-197902000-00006 ↗
23. Ultrastructural identification of a benign perineurial cell tumor10.1002/1097-0142(197805)41:5<1823::aid-cncr2820410525>3.0.co;2-j ↗
24. Alterations of DNA methylation associated with abnormalities of DNA methyltransferases in human cancers during transition from a precancerous to a malignant state10.1093/carcin/bgm206 ↗
25. Mathematical models of tumor cell proliferation: A review of the literature10.1080/14737140.2018.1527689 ↗