Low-grade gliomas (LGGs) are brain tumors characterized by their slow growth and infiltrative nature. Treatment options for these tumors are surgery, radiation therapy and chemotherapy. The optimal use of radiation therapy and chemotherapy is still under study. In this paper, we construct a mathematical model of LGG response to combinations of chemotherapy, specifically to the alkylating agent temozolomide and radiation therapy. Patient-specific parameters were obtained from longitudinal imaging data of the response of real LGG patients. Computer simulations showed that concurrent cycles of radiation therapy and temozolomide could provide the best therapeutic efficacy in-silico for the patients included in the study. The patient cohort was extended computationally to a set of 3000 virtual patients. This virtual cohort was subject to an in-silico trial in which matching the doses of radiotherapy to those of temozolomide in the first five days of each cycle improved overall survival over concomitant radio-chemotherapy according to RTOG 0424. Thus, the proposed treatment schedule could be investigated in a clinical setting to improve combination treatments in LGGs with substantial survival benefits.

We study the dynamics of multistable coexisting rotating waves that propagate along a unidirectional ring consisting of coupled double-well Duffing oscillators with different numbers of oscillators. By employing time series analysis, phase portraits, bifurcation diagrams, and basins of attraction, we provide evidence of multistability on the route from coexisting stable equilibria to hyperchaos via a sequence of bifurcations, including the Hopf bifurcation, torus bifurcations, and crisis bifurcations, as the coupling strength is increased. The specific bifurcation route depends on whether the ring comprises an even or odd number of oscillators. In the case of an even number of oscillators, we observe the existence of up to 32 coexisting stable fixed points at relatively weak coupling strengths, while a ring with an odd number of oscillators exhibits 20 coexisting stable equilibria. As the coupling strength increases, a hidden amplitude death attractor is born in an inverse supercritical pitchfork bifurcation in the ring with an even number of oscillators, coexisting with various homoclinic and heteroclinic orbits. Additionally, for stronger coupling, amplitude death coexists with chaos. Notably, the rotating wave speed of all coexisting limit cycles remains approximately constant and undergoes an exponential decrease as the coupling strength is increased. At the same time, the wave frequency varies among different coexisting orbits, exhibiting an almost linear growth with the coupling strength. It is worth mentioning that orbits originating from stronger coupling strengths possess higher frequencies.

We use the Hirota bilinear technique to investigate wave solutions to the Heisenberg ferromagnetic- type Akbota problem arising in surface geometry. The equation is a crucial paradigm for examining and visualizing surface geometry and curve analysis. The equation is an integrable coupled model with soliton solutions. It is a key instrument for investigating nonlinear phenomena in differential geometry of curves and surfaces, magnetism, and optics. The solutions we explore are periodic lump waves, periodic cross-kink waves, homoclinic breather waves, M-shaped waves interacting with kink and rogue waves, and mixed waves. We derive exact solutions and carefully choose parameter values to generate a variety of three-dimensional graphs and the associated contour and density plots. The soliton phenomenon is explained by the physical structures and solutions discovered, which also replicate the dynamic characteristics of the traveling-wave deformation front that is created in the dispersive medium. It demonstrates the power, suitability, and potential applications of the Hirota bilinear technique in future research toidentify unique solutions for a wide range of nonlinear model types found in engineering and physicalscience. These solutions are relevant in nonlinear fiber optics, magnetism and differential geometry.