Research starts with PhD students

Chapter 36 Congratulations, your paper has passed!
Target solution transformation of the nonlinear Schrödinger equation.

A transformation method used in particle physics experiments to analyze the Schrödinger equation, with the goal of finding an exact solution or a region of solutions.

Transformation actually means narrowing the range of solutions to the equation.

For example, the original equation has ten solutions, but after the transformation the range of solutions is greatly reduced, and there may only be one or two solutions.

So the transformed equation is different from the original equation.

For example, X=2Y is a straight line on a plane, and any coordinates on the line are a set of solutions.

The target solution transformation can be simply understood as substituting numerical values ​​and setting X=2, then Y can only be equal to 1.

The final result is a coordinate point.

The transformation process is to narrow the range of the solution. The latter is not equivalent to the former. Using conventional mathematical logic to analyze, the transformation process is wrong, but it can help find a set of solutions faster, or analyze the area of ​​a set of solutions.

This is a method developed for experimental analysis.

A large number of computational problems will be encountered in the experiment, but for the nonlinear Schrödinger equation, it is not necessary to find all the exact solutions, only a set of solutions or a region of solutions is needed.

This method is widely used in physical experiments that require large-scale data analysis.

But, the professors don’t know?

"Is it because of the differences in the world? Are there differences in the progress of some academic research?" Zhang Shuo thought of the method of transforming system of equations.

When he was doing data work at the experimental base of the Institute of High Energy Physics, he used the method of equation transformation. Luo Yongjun said he didn't know about it and thought it was a new research.

"So, the difference is still reflected in the research level of theoretical physics and particle physics."

"Whether it is the equation transformation method or the target solution conversion method, both are methods used to analyze a large amount of particle data."

"This world does not exist, and it is likely caused by the gap in theoretical physics and particle physics research."

"If there are applications, then research will be done. If there are few applications, there will be little research."

The particle experiment analysis in the previous life confirmed the existence of "unknown physical phenomena", and later several physical theories emerged to specifically study and analyze this phenomenon.

"The Theory of Source Point" is one of them.

Many scientific research institutions hope to verify new physical theories through experiments.

Zhang Shuo’s team is one of them.

When a lot of scientific research resources are invested in one direction, related academic research will also make progress, for example, the computational mathematics and analytical algorithms used in particle data analysis.

In classrooms.

A lot of thoughts flashed through Zhang Shuo's mind, but he looked a little overwhelmed because he was squeezed into the corner of the desk.

He was sitting against the wall.

Qi Zhixiang, Tong Jie, and Su Bingkang surrounded him, the other professors stood behind him, and there were a dozen doctoral students watching.

This situation made Zhang Shuo not know how to start.

Qi Zhixiang kept staring at Zhang Shuo, waiting for the explanation of the problem-solving process in the draft book.

Tong Jie was the first to react. "With so many people around, Zhang Shuo can still speak." She then asked Zhang Shuo, "How about we speak on the podium?"

"Yep!"

Qi Zhixiang and Su Bingkang also reacted and immediately made way for him. "Student Zhang Shuo, please go to the podium and tell us about this problem."

"We will be the students and you will be the teacher."

"If you don't explain it clearly, I really can't sleep..."

Other professors followed suit.

They enthusiastically escorted Zhang Shuo to the podium and then found a seat in the front row of the classroom.

The doctoral students also found their seats and sat down.

They didn't expect that they would be able to watch a big show after the course.

Several high-ranking mathematics professors are actually willing to be students and let their doctoral students explain math problems to them?
……

On the podium.

Zhang Shuo seemed very relaxed, since he was not giving an academic report and did not need to pay much attention to etiquette, he just read the draft normally.

He thought about it, copied the part before the conversion on the blackboard, copied the function of the previous part, and drew a graphical comparison next to it.

Then, he turned around to confirm, "This is the part, right?"

"Yes."

"right here!"

Qi Zhixiang and Su Bingkang were both sitting in the first row. They immediately nodded in agreement, their eyes gleaming with a thirst for knowledge.

Qi Zhixiang also added a question, "We don't understand why the wrong transformation can produce an exact solution?"

“This is a special case.”

Zhang Shuo emphasized, "Most nonlinear Schrödinger equations do not have exact solutions. In the process of solving them, I am not sure whether there are exact solutions."

"But even if it doesn't exist, we can find a range of solutions."

He continued, "You should have seen the solution process in this book. I only used one step to convert it."

“So, the process is simple.”

Zhang Shuo talked about the transformation process. "It is called transformation, but in fact it is a simplification of the analysis results." He wrote down various parameters and explained the changes one by one.

"This coordinate can be directly obtained."

“Here, you can directly plug in the value and get the result by mental arithmetic.”

“Look at this function!”

He pointed at the function he had written down and said, "Just plug it in. The parameters include the coordinate points. Just plug them in and transform them directly."

"Then, it came out..."

Zhang Shuo quickly calculated the next step, and the result was the same as the transformation in the draft book. The professors were a little confused.

They finally understood why the transformation was completed in one step. All the calculations in the transformation process were done mentally, and the functions referenced earlier were also directly brought in and transformed.

But why?

How can you do this!

Zhang Shuo turned to face the classroom and explained, "I am not doing equation analysis. My goal is very direct, which is to find a set of exact solutions or a set of solution regions."

“Just like the numerical method, it actually means the same thing.”

"The conventional equation-solving process requires rigor, and the goal is to conduct a complete analysis of the equation and find all the solutions."

“But I only want one set of solutions.”

Several professors suddenly realized.

Different purposes!

The goal of solving general equations is to find all solutions. The process must be very rigorous and there cannot be the slightest error.

The current goal is to find a set of solutions, the principle of which is a bit like the numerical method, but more extreme than the numerical method.

This transformation method is also completely applicable to the Schrödinger equation.

If it is another type of equation, it cannot be transformed according to the function analyzed previously due to the different nature of the parameters.

Everyone understands.

Qi Zhixiang was the first to stand up and exclaimed, "This method is not difficult, but the angle of thinking is very interesting, and it only applies to the Schrödinger equation."

"But even if we study the Schrödinger equation, it's hard to come up with a solution..."

He asked Zhang Shuo, "Is this your own research?"

"Yes."

Zhang Shuo hesitated for a moment, but finally nodded in agreement.

"The future is terrifying!"

Qi Zhixiang patted Zhang Shuo on the shoulder and said seriously, "I feel like what you said is only part of the research."

"This research is very interesting. Hurry up and write the paper."

"This is about computational mathematics. There should be no problem in submitting it to SCI Zone 3 in computational mathematics. If you can supplement or expand the content, you may also have a chance in Zone 2."

Other professors also came over and said, “Yes, you can write your paper now.”

“This method has certain application value!”

"It's mainly because I think from a different perspective. It really opened my eyes. I never thought that I could calculate in this way..."

They left in admiration.

When they reached the door, Qi Zhixiang suddenly turned around and asked, "Your advisor is Professor Luo Yongjun, right?"

"Correct."

"very nice."

Qi Zhixiang commented with a somewhat confusing smile.

……

After the course, Zhang Shuo returned to the dormitory and was once again "besieged" by Huang Kai and Liu Chengjie.

“So, there’s another paper?”

"You can still vote for District 2!"

"Do you know who Professor Qi is? He's a researcher at the Academy of Sciences and has contributed to the four major mathematics journals!"

"You actually taught him mathematics..."

"Ugh."

"We are really not in the same world!"

Liu Chengjie said, "You have an algorithm paper on high-energy physics, and submit a mathematics paper in zone three or even zone two..."

“It’s a bit of a loss!”

"I think you can treat it as a graduation thesis? That way you don't have to think about the content of the graduation thesis."

"No need, it's just... ahem." Zhang Shuo wanted to say it was just a small thing, but it seemed a bit discouraging, so he just shook his head and continued looking at the computer.

I opened my mailbox and received a new email from Friedrich Jost.

“I’m glad to see your reply, especially since what you said is consistent with my judgment, which shows that I am not too old to lose my judgment.

You have done remarkable research.

I believe that after the paper is published, it will definitely shock the mathematics community. Engineers who are engaged in PDE calculations may find it easier in the future, as they will have efficient software to assist in calculations.

That’s right, congratulations, your paper has passed!
Maxim and I are your reviewers, and we have already written our comments on the paper..."

Zhang Shuo finished reading the email carefully, turned around and found Huang Kai also staring at it. He pointed at the name on the screen and asked, "Whose email is it? Maxim?"

"Who?"

Zhang Shuo closed his email and said nonchalantly, "Editor of High Energy Physics Journal, please discuss the issue of paper publication with me."

Huang Kai immediately lost interest.

Zhang Shuo pursed his lips tightly and found that he still had to tell more white lies so as not to hurt others!
Doorway.

When Liu Chengjie heard the conversation between the two, he couldn't help but mutter, "Maxim? Maxim, Maxim...seems familiar?"

"I seem to have heard it somewhere..."

(End of this chapter)